Solve x^2+12^2=16^2

$${ x }^{ 2 } + { 12 }^{ 2 } = { 16 }^{ 2 }$$

Solve for x

$$x=4\sqrt{7}\approx 10.583005244$$

$$x=-4\sqrt{7}\approx -10.583005244$$

Steps by Finding Square Root

Calculate 12 to the power of 2 and get 144.

$$x^{2}+144=16^{2}$$

Calculate 16 to the power of 2 and get 256.

$$x^{2}+144=256$$

Subtract 144 from both sides.

$$x^{2}=256-144$$

Subtract 144 from 256 to get 112.

$$x^{2}=112$$

Take the square root of both sides of the equation.

$$x=4\sqrt{7} x=-4\sqrt{7}$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 2 and get 144.

$$x^{2}+144=16^{2}$$

Calculate 16 to the power of 2 and get 256.

$$x^{2}+144=256$$

Subtract 256 from both sides.

$$x^{2}+144-256=0$$

Subtract 256 from 144 to get -112.

$$x^{2}-112=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -112 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-112\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-112\right)}}{2}$$

Multiply -4 times -112.

$$x=\frac{0±\sqrt{448}}{2}$$

Take the square root of 448.

$$x=\frac{0±8\sqrt{7}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{7}}{2} when ± is plus.

$$x=4\sqrt{7}$$

Now solve the equation x=\frac{0±8\sqrt{7}}{2} when ± is minus.

$$x=-4\sqrt{7}$$

The equation is now solved.

$$x=4\sqrt{7} x=-4\sqrt{7}$$