Solve x^2=12^2+6^2

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

Solve for x

$$x=6\sqrt{5}\approx 13.416407865$$

$$x=-6\sqrt{5}\approx -13.416407865$$

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.

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

Add 144 and 36 to get 180.

$$x^{2}=180$$

Take the square root of both sides of the equation.

$$x=6\sqrt{5} x=-6\sqrt{5}$$

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.

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

Add 144 and 36 to get 180.

$$x^{2}=180$$

Subtract 180 from both sides.

$$x^{2}-180=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -180 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-180\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-180\right)}}{2}$$

Multiply -4 times -180.

$$x=\frac{0±\sqrt{720}}{2}$$

Take the square root of 720.

$$x=\frac{0±12\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±12\sqrt{5}}{2} when ± is plus.

$$x=6\sqrt{5}$$

Now solve the equation x=\frac{0±12\sqrt{5}}{2} when ± is minus.

$$x=-6\sqrt{5}$$

The equation is now solved.

$$x=6\sqrt{5} x=-6\sqrt{5}$$