Solve x^2-24^2+8=0

$${ x }^{ 2 } - { 24 }^{ 2 } +8 = 0$$

Solve for x

$$x=2\sqrt{142}\approx 23.832750576$$

$$x=-2\sqrt{142}\approx -23.832750576$$

Steps by Finding Square Root

Calculate 24 to the power of 2 and get 576.

$$x^{2}-576+8=0$$

Add -576 and 8 to get -568.

$$x^{2}-568=0$$

Add 568 to both sides. Anything plus zero gives itself.

$$x^{2}=568$$

Take the square root of both sides of the equation.

$$x=2\sqrt{142} x=-2\sqrt{142}$$

Steps Using the Quadratic Formula

Calculate 24 to the power of 2 and get 576.

$$x^{2}-576+8=0$$

Add -576 and 8 to get -568.

$$x^{2}-568=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -568 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-568\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-568\right)}}{2}$$

Multiply -4 times -568.

$$x=\frac{0±\sqrt{2272}}{2}$$

Take the square root of 2272.

$$x=\frac{0±4\sqrt{142}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{142}}{2} when ± is plus.

$$x=2\sqrt{142}$$

Now solve the equation x=\frac{0±4\sqrt{142}}{2} when ± is minus.

$$x=-2\sqrt{142}$$

The equation is now solved.

$$x=2\sqrt{142} x=-2\sqrt{142}$$