Solve x^2+4^2=16^2

$$x ^ { 2 } + 4 ^ { 2 } = 16 ^ { 2 }$$

Solve for x

$$x=4\sqrt{15}\approx 15.491933385$$

$$x=-4\sqrt{15}\approx -15.491933385$$

Steps by Finding Square Root

Calculate 4 to the power of 2 and get 16.

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

Calculate 16 to the power of 2 and get 256.

$$x^{2}+16=256$$

Subtract 16 from both sides.

$$x^{2}=256-16$$

Subtract 16 from 256 to get 240.

$$x^{2}=240$$

Take the square root of both sides of the equation.

$$x=4\sqrt{15} x=-4\sqrt{15}$$

Steps Using the Quadratic Formula

Calculate 4 to the power of 2 and get 16.

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

Calculate 16 to the power of 2 and get 256.

$$x^{2}+16=256$$

Subtract 256 from both sides.

$$x^{2}+16-256=0$$

Subtract 256 from 16 to get -240.

$$x^{2}-240=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -240 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-240\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-240\right)}}{2}$$

Multiply -4 times -240.

$$x=\frac{0±\sqrt{960}}{2}$$

Take the square root of 960.

$$x=\frac{0±8\sqrt{15}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{15}}{2} when ± is plus.

$$x=4\sqrt{15}$$

Now solve the equation x=\frac{0±8\sqrt{15}}{2} when ± is minus.

$$x=-4\sqrt{15}$$

The equation is now solved.

$$x=4\sqrt{15} x=-4\sqrt{15}$$