Solve x^2+8=75

$${ x }^{ 2 } +8=75$$

Solve for x

$$x=\sqrt{67}\approx 8.185352772$$

$$x=-\sqrt{67}\approx -8.185352772$$

Steps by Finding Square Root

Subtract 8 from both sides.

$$x^{2}=75-8$$

Subtract 8 from 75 to get 67.

$$x^{2}=67$$

Take the square root of both sides of the equation.

$$x=\sqrt{67} x=-\sqrt{67}$$

Steps Using the Quadratic Formula

Subtract 75 from both sides.

$$x^{2}+8-75=0$$

Subtract 75 from 8 to get -67.

$$x^{2}-67=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -67 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-67\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-67\right)}}{2}$$

Multiply -4 times -67.

$$x=\frac{0±\sqrt{268}}{2}$$

Take the square root of 268.

$$x=\frac{0±2\sqrt{67}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{67}}{2} when ± is plus.

$$x=\sqrt{67}$$

Now solve the equation x=\frac{0±2\sqrt{67}}{2} when ± is minus.

$$x=-\sqrt{67}$$

The equation is now solved.

$$x=\sqrt{67} x=-\sqrt{67}$$