Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x-180=6688/19
- Equation sqrt(2x+63)=-x
- Equation x^2-4i=0
- Equation √7x-5-√3x-2=√4x-3
- Express {x} in terms of y where:
- 4*x-16*y=6
- -14*x-1*y=3
- 8*x+7*y=-13
- 5*x+5*y=20
- Derivative of:
-
-x
- Integral of d{x}:
-
-x
- Graphing y =:
- -x
-
Identical expressions
- sqrt(2x+ sixty-three)=-x
- square root of (2x plus 63) equally minus x
- square root of (2x plus sixty minus three) equally minus x
- √(2x+63)=-x
- sqrt2x+63=-x
-
Similar expressions
- sqrt(2x+63)=+x
- sqrt(2x-63)=-x
sqrt(2x+63)=-x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{2 x + 63} = - x$$
$$\sqrt{2 x + 63} = - x$$
We raise the equation sides to 2-th degree
$$2 x + 63 = x^{2}$$
$$2 x + 63 = x^{2}$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} + 2 x + 63 = 0$$
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
$$a = -1$$
$$b = 2$$
$$c = 63$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -7$$
$$x_{2} = 9$$
Because
$$\sqrt{2 x + 63} = - x$$
and
$$\sqrt{2 x + 63} \geq 0$$
then
$$- x \geq 0$$
or
$$x \leq 0$$
$$-\infty < x$$
The final answer:
$$x_{1} = -7$$
$$\sqrt{2 x + 63} = - x$$
$$\sqrt{2 x + 63} = - x$$
We raise the equation sides to 2-th degree
$$2 x + 63 = x^{2}$$
$$2 x + 63 = x^{2}$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} + 2 x + 63 = 0$$
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
$$a = -1$$
$$b = 2$$
$$c = 63$$
, then
D = b^2 - 4 * a * c =
(2)^2 - 4 * (-1) * (63) = 256
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -7$$
$$x_{2} = 9$$
Because
$$\sqrt{2 x + 63} = - x$$
and
$$\sqrt{2 x + 63} \geq 0$$
then
$$- x \geq 0$$
or
$$x \leq 0$$
$$-\infty < x$$
The final answer:
$$x_{1} = -7$$