Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2x^2-8=0
-
Equation 8x-15=-12+5x
-
Equation 2x-2=0
-
Equation (x-4)²+(x+9)²=2x²
- Express {x} in terms of y where:
- 12*x+1*y=11
- 11*x-6*y=1
- 8*x-1*y=18
- -17*x-6*y=1
- Derivative of:
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sqrt(1-2x)
- Graphing y =:
- sqrt(1-2x)
- Integral of d{x}:
- sqrt(1-2x)
-
Identical expressions
- sqrt(one -2x)=a-7absolute(x)
- square root of (1 minus 2x) equally a minus 7absolute(x)
- square root of (one minus 2x) equally a minus 7absolute(x)
- √(1-2x)=a-7absolute(x)
- sqrt1-2x=a-7absolutex
-
Similar expressions
- sqrt(1-2x)=a+7absolute(x)
- sqrt(1-2x)=a-7absolutex
- -x^2/sqrt(1-2*x)+2*x*sqrt(1-2*x)=0
- sqrt(1+2x)=a-7absolute(x)
sqrt(1-2x)=a-7absolute(x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x \geq 0$$
or
$$0 \leq x \wedge x < \infty$$
we get the equation
$$- a + 7 x + \sqrt{1 - 2 x} = 0$$
after simplifying we get
$$- a + 7 x + \sqrt{1 - 2 x} = 0$$
the solution in this interval:
$$x_{1} = \frac{a}{7} - \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49}$$
$$x_{2} = \frac{a}{7} + \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49}$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$- a + 7 \left(- x\right) + \sqrt{1 - 2 x} = 0$$
after simplifying we get
$$- a - 7 x + \sqrt{1 - 2 x} = 0$$
the solution in this interval:
$$x_{3} = - \frac{a}{7} - \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49}$$
$$x_{4} = - \frac{a}{7} + \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49}$$
The final answer:
$$x_{1} = \frac{a}{7} - \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49}$$
$$x_{2} = \frac{a}{7} + \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49}$$
$$x_{3} = - \frac{a}{7} - \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49}$$
$$x_{4} = - \frac{a}{7} + \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49}$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x \geq 0$$
or
$$0 \leq x \wedge x < \infty$$
we get the equation
$$- a + 7 x + \sqrt{1 - 2 x} = 0$$
after simplifying we get
$$- a + 7 x + \sqrt{1 - 2 x} = 0$$
the solution in this interval:
$$x_{1} = \frac{a}{7} - \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49}$$
$$x_{2} = \frac{a}{7} + \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49}$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$- a + 7 \left(- x\right) + \sqrt{1 - 2 x} = 0$$
after simplifying we get
$$- a - 7 x + \sqrt{1 - 2 x} = 0$$
the solution in this interval:
$$x_{3} = - \frac{a}{7} - \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49}$$
$$x_{4} = - \frac{a}{7} + \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49}$$
The final answer:
$$x_{1} = \frac{a}{7} - \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49}$$
$$x_{2} = \frac{a}{7} + \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49}$$
$$x_{3} = - \frac{a}{7} - \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49}$$
$$x_{4} = - \frac{a}{7} + \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49}$$
The graph
Sum and product of roots
[src]
sum
// ___________ ___ __________ \ // ___________ ___ __________ \ // ___________ ___ __________ \ // ___________ ___ __________ \ // ___________ ___ __________ \ // ___________ ___ __________ \ // ___________ ___ __________ \ // ___________ ___ __________ \
|| 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a | || 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a | || 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a | || 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a | || 1 \/ 50 - 14*a a 1 a \/ 2 *\/ 25 - 7*a | || 1 \/ 50 - 14*a a 1 a \/ 2 *\/ 25 - 7*a | || 1 a \/ 50 - 14*a 1 a \/ 2 *\/ 25 - 7*a | || 1 a \/ 50 - 14*a 1 a \/ 2 *\/ 25 - 7*a |
||- -- - - - ------------- for -- + - + ------------------ > 0| ||- -- - - - ------------- for -- + - + ------------------ > 0| ||- -- - - + ------------- for -- + - - ------------------ > 0| ||- -- - - + ------------- for -- + - - ------------------ > 0| ||- -- - ------------- + - for -- - - + ------------------ <= 0| ||- -- - ------------- + - for -- - - + ------------------ <= 0| ||- -- + - + ------------- for - -- + - + ------------------ >= 0| ||- -- + - + ------------- for - -- + - + ------------------ >= 0|
I*im|< 49 7 49 49 7 49 | + re|< 49 7 49 49 7 49 | + I*im|< 49 7 49 49 7 49 | + re|< 49 7 49 49 7 49 | + I*im|< 49 49 7 49 7 49 | + re|< 49 49 7 49 7 49 | + I*im|< 49 7 49 49 7 49 | + re|< 49 7 49 49 7 49 |
|| | || | || | || | || | || | || | || |
|| nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise |
\\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ /
$$\left(\left(\left(\operatorname{re}{\left(\begin{cases} - \frac{a}{7} - \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{7} - \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) + \left(\operatorname{re}{\left(\begin{cases} - \frac{a}{7} + \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} - \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{7} + \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} - \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)\right) + \left(\operatorname{re}{\left(\begin{cases} \frac{a}{7} - \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: - \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} + \frac{1}{49} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{7} - \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: - \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} + \frac{1}{49} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)\right) + \left(\operatorname{re}{\left(\begin{cases} \frac{a}{7} + \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} - \frac{1}{49} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{7} + \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} - \frac{1}{49} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
// ___________ ___ __________ \ // ___________ ___ __________ \ // ___________ ___ __________ \ // ___________ ___ __________ \ // ___________ ___ __________ \ // ___________ ___ __________ \ // ___________ ___ __________ \ // ___________ ___ __________ \
|| 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a | || 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a | || 1 \/ 50 - 14*a a 1 a \/ 2 *\/ 25 - 7*a | || 1 a \/ 50 - 14*a 1 a \/ 2 *\/ 25 - 7*a | || 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a | || 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a | || 1 \/ 50 - 14*a a 1 a \/ 2 *\/ 25 - 7*a | || 1 a \/ 50 - 14*a 1 a \/ 2 *\/ 25 - 7*a |
||- -- - - - ------------- for -- + - + ------------------ > 0| ||- -- - - + ------------- for -- + - - ------------------ > 0| ||- -- - ------------- + - for -- - - + ------------------ <= 0| ||- -- + - + ------------- for - -- + - + ------------------ >= 0| ||- -- - - - ------------- for -- + - + ------------------ > 0| ||- -- - - + ------------- for -- + - - ------------------ > 0| ||- -- - ------------- + - for -- - - + ------------------ <= 0| ||- -- + - + ------------- for - -- + - + ------------------ >= 0|
I*im|< 49 7 49 49 7 49 | + I*im|< 49 7 49 49 7 49 | + I*im|< 49 49 7 49 7 49 | + I*im|< 49 7 49 49 7 49 | + re|< 49 7 49 49 7 49 | + re|< 49 7 49 49 7 49 | + re|< 49 49 7 49 7 49 | + re|< 49 7 49 49 7 49 |
|| | || | || | || | || | || | || | || |
|| nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise |
\\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ /
$$\operatorname{re}{\left(\begin{cases} - \frac{a}{7} - \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} - \frac{a}{7} + \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} - \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} \frac{a}{7} - \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: - \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} + \frac{1}{49} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} \frac{a}{7} + \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} - \frac{1}{49} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{7} - \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{7} + \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} - \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{7} - \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: - \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} + \frac{1}{49} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{7} + \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} - \frac{1}{49} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
product
/ // ___________ ___ __________ \ // ___________ ___ __________ \\ / // ___________ ___ __________ \ // ___________ ___ __________ \\ / // ___________ ___ __________ \ // ___________ ___ __________ \\ / // ___________ ___ __________ \ // ___________ ___ __________ \\ | || 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a | || 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a || | || 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a | || 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a || | || 1 \/ 50 - 14*a a 1 a \/ 2 *\/ 25 - 7*a | || 1 \/ 50 - 14*a a 1 a \/ 2 *\/ 25 - 7*a || | || 1 a \/ 50 - 14*a 1 a \/ 2 *\/ 25 - 7*a | || 1 a \/ 50 - 14*a 1 a \/ 2 *\/ 25 - 7*a || | ||- -- - - - ------------- for -- + - + ------------------ > 0| ||- -- - - - ------------- for -- + - + ------------------ > 0|| | ||- -- - - + ------------- for -- + - - ------------------ > 0| ||- -- - - + ------------- for -- + - - ------------------ > 0|| | ||- -- - ------------- + - for -- - - + ------------------ <= 0| ||- -- - ------------- + - for -- - - + ------------------ <= 0|| | ||- -- + - + ------------- for - -- + - + ------------------ >= 0| ||- -- + - + ------------- for - -- + - + ------------------ >= 0|| |I*im|< 49 7 49 49 7 49 | + re|< 49 7 49 49 7 49 ||*|I*im|< 49 7 49 49 7 49 | + re|< 49 7 49 49 7 49 ||*|I*im|< 49 49 7 49 7 49 | + re|< 49 49 7 49 7 49 ||*|I*im|< 49 7 49 49 7 49 | + re|< 49 7 49 49 7 49 || | || | || || | || | || || | || | || || | || | || || | || nan otherwise | || nan otherwise || | || nan otherwise | || nan otherwise || | || nan otherwise | || nan otherwise || | || nan otherwise | || nan otherwise || \ \\ / \\ // \ \\ / \\ // \ \\ / \\ // \ \\ / \\ //
$$\left(\operatorname{re}{\left(\begin{cases} - \frac{a}{7} - \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{7} - \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} - \frac{a}{7} + \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} - \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{7} + \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} - \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} \frac{a}{7} - \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: - \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} + \frac{1}{49} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{7} - \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: - \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} + \frac{1}{49} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} \frac{a}{7} + \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} - \frac{1}{49} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{7} + \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} - \frac{1}{49} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
/ 4 4 2 2 2 2 3 3 |1 + im (a) + re (a) - 2*re (a) + 2*im (a) - 6*im (a)*re (a) - 4*I*im (a)*re(a) - 4*I*im(a)*re(a) + 4*I*re (a)*im(a) |------------------------------------------------------------------------------------------------------------------- for And(a <= 25/7, a > 1) < 2401 | | nan otherwise \
$$\begin{cases} \frac{\left(\operatorname{re}{\left(a\right)}\right)^{4} + 4 i \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 i \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 i \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1}{2401} & \text{for}\: a \leq \frac{25}{7} \wedge a > 1 \\\text{NaN} & \text{otherwise} \end{cases}$$
Piecewise(((1 + im(a)^4 + re(a)^4 - 2*re(a)^2 + 2*im(a)^2 - 6*im(a)^2*re(a)^2 - 4*i*im(a)^3*re(a) - 4*i*im(a)*re(a) + 4*i*re(a)^3*im(a))/2401, (a <= 25/7)∧(a > 1)), (nan, True))
Rapid solution
[src]
// ___________ ___ __________ \ // ___________ ___ __________ \
|| 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a | || 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a |
||- -- - - - ------------- for -- + - + ------------------ > 0| ||- -- - - - ------------- for -- + - + ------------------ > 0|
x1 = I*im|< 49 7 49 49 7 49 | + re|< 49 7 49 49 7 49 |
|| | || |
|| nan otherwise | || nan otherwise |
\\ / \\ /
$$x_{1} = \operatorname{re}{\left(\begin{cases} - \frac{a}{7} - \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{7} - \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
// ___________ ___ __________ \ // ___________ ___ __________ \
|| 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a | || 1 a \/ 50 + 14*a 1 a \/ 2 *\/ 25 + 7*a |
||- -- - - + ------------- for -- + - - ------------------ > 0| ||- -- - - + ------------- for -- + - - ------------------ > 0|
x2 = I*im|< 49 7 49 49 7 49 | + re|< 49 7 49 49 7 49 |
|| | || |
|| nan otherwise | || nan otherwise |
\\ / \\ /
$$x_{2} = \operatorname{re}{\left(\begin{cases} - \frac{a}{7} + \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} - \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{7} + \frac{\sqrt{14 a + 50}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} - \frac{\sqrt{2} \sqrt{7 a + 25}}{49} + \frac{1}{49} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
// ___________ ___ __________ \ // ___________ ___ __________ \
|| 1 \/ 50 - 14*a a 1 a \/ 2 *\/ 25 - 7*a | || 1 \/ 50 - 14*a a 1 a \/ 2 *\/ 25 - 7*a |
||- -- - ------------- + - for -- - - + ------------------ <= 0| ||- -- - ------------- + - for -- - - + ------------------ <= 0|
x3 = I*im|< 49 49 7 49 7 49 | + re|< 49 49 7 49 7 49 |
|| | || |
|| nan otherwise | || nan otherwise |
\\ / \\ /
$$x_{3} = \operatorname{re}{\left(\begin{cases} \frac{a}{7} - \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: - \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} + \frac{1}{49} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{7} - \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: - \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} + \frac{1}{49} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
// ___________ ___ __________ \ // ___________ ___ __________ \
|| 1 a \/ 50 - 14*a 1 a \/ 2 *\/ 25 - 7*a | || 1 a \/ 50 - 14*a 1 a \/ 2 *\/ 25 - 7*a |
||- -- + - + ------------- for - -- + - + ------------------ >= 0| ||- -- + - + ------------- for - -- + - + ------------------ >= 0|
x4 = I*im|< 49 7 49 49 7 49 | + re|< 49 7 49 49 7 49 |
|| | || |
|| nan otherwise | || nan otherwise |
\\ / \\ /
$$x_{4} = \operatorname{re}{\left(\begin{cases} \frac{a}{7} + \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} - \frac{1}{49} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{7} + \frac{\sqrt{50 - 14 a}}{49} - \frac{1}{49} & \text{for}\: \frac{a}{7} + \frac{\sqrt{2} \sqrt{25 - 7 a}}{49} - \frac{1}{49} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
x4 = re(Piecewise((a/7 + sqrt(50 - 14*a/49 - 1/49, a/7 + sqrt(2)*sqrt(25 - 7*a)/49 - 1/49 >= 0), (nan, True))) + i*im(Piecewise((a/7 + sqrt(50 - 14*a)/49 - 1/49, a/7 + sqrt(2)*sqrt(25 - 7*a)/49 - 1/49 >= 0), (nan, True))))