Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 2x^2-8=0
-
Equation x^2-3x+5=0
-
Equation x^2+10*x+24=0
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Equation (x-8)^2=(x-2)^2
- Express {x} in terms of y where:
- -14*x-3*y=-14
- 4*x-8*y=10
- -19*x-5*y=-5
- -1*x-14*y=5
- Derivative of:
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-x
- Integral of d{x}:
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-x
- Limit of the function:
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-x
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Identical expressions
- sqrt(seven - three *x)- one =-x
- square root of (7 minus 3 multiply by x) minus 1 equally minus x
- square root of (seven minus three multiply by x) minus one equally minus x
- √(7-3*x)-1=-x
- sqrt(7-3x)-1=-x
- sqrt7-3x-1=-x
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Similar expressions
- sqrt(7-3*x)+1=-x
- sqrt(7-3*x)-1=+x
- sqrt(7+3*x)-1=-x
- 15-(x-4)=5
sqrt(7-3*x)-1=-x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{7 - 3 x} - 1 = - x$$
$$\sqrt{7 - 3 x} = 1 - x$$
We raise the equation sides to 2-th degree
$$7 - 3 x = \left(1 - x\right)^{2}$$
$$7 - 3 x = x^{2} - 2 x + 1$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} - x + 6 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -1$$
$$b = -1$$
$$c = 6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -3$$
$$x_{2} = 2$$
Because
$$\sqrt{7 - 3 x} = 1 - x$$
and
$$\sqrt{7 - 3 x} \geq 0$$
then
$$1 - x \geq 0$$
or
$$x \leq 1$$
$$-\infty < x$$
The final answer:
$$x_{1} = -3$$
$$\sqrt{7 - 3 x} - 1 = - x$$
$$\sqrt{7 - 3 x} = 1 - x$$
We raise the equation sides to 2-th degree
$$7 - 3 x = \left(1 - x\right)^{2}$$
$$7 - 3 x = x^{2} - 2 x + 1$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} - x + 6 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -1$$
$$b = -1$$
$$c = 6$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (-1) * (6) = 25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -3$$
$$x_{2} = 2$$
Because
$$\sqrt{7 - 3 x} = 1 - x$$
and
$$\sqrt{7 - 3 x} \geq 0$$
then
$$1 - x \geq 0$$
or
$$x \leq 1$$
$$-\infty < x$$
The final answer:
$$x_{1} = -3$$