Solve x^2=12^2-6^2

$$x ^ { 2 } = 12 ^ { 2 } - 6 ^ { 2 }$$

Solve for x

$$x=6\sqrt{3}\approx 10.392304845$$

$$x=-6\sqrt{3}\approx -10.392304845$$

Steps by Finding Square Root

Calculate 12 to the power of 2 and get 144.

$$x^{2}=144-6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$x^{2}=144-36$$

Subtract 36 from 144 to get 108.

$$x^{2}=108$$

Take the square root of both sides of the equation.

$$x=6\sqrt{3} x=-6\sqrt{3}$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 2 and get 144.

$$x^{2}=144-6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$x^{2}=144-36$$

Subtract 36 from 144 to get 108.

$$x^{2}=108$$

Subtract 108 from both sides.

$$x^{2}-108=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -108 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-108\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-108\right)}}{2}$$

Multiply -4 times -108.

$$x=\frac{0±\sqrt{432}}{2}$$

Take the square root of 432.

$$x=\frac{0±12\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±12\sqrt{3}}{2} when ± is plus.

$$x=6\sqrt{3}$$

Now solve the equation x=\frac{0±12\sqrt{3}}{2} when ± is minus.

$$x=-6\sqrt{3}$$

The equation is now solved.

$$x=6\sqrt{3} x=-6\sqrt{3}$$