Solve x^2+200^2=460^2

$${ x }^{ 2 } + { 200 }^{ 2 } = { 460 }^{ 2 }$$

Solve for x

$$x=20\sqrt{429}\approx 414.246303544$$

$$x=-20\sqrt{429}\approx -414.246303544$$

Steps by Finding Square Root

Calculate 200 to the power of 2 and get 40000.

$$x^{2}+40000=460^{2}$$

Calculate 460 to the power of 2 and get 211600.

$$x^{2}+40000=211600$$

Subtract 40000 from both sides.

$$x^{2}=211600-40000$$

Subtract 40000 from 211600 to get 171600.

$$x^{2}=171600$$

Take the square root of both sides of the equation.

$$x=20\sqrt{429} x=-20\sqrt{429}$$

Steps Using the Quadratic Formula

Calculate 200 to the power of 2 and get 40000.

$$x^{2}+40000=460^{2}$$

Calculate 460 to the power of 2 and get 211600.

$$x^{2}+40000=211600$$

Subtract 211600 from both sides.

$$x^{2}[phone]=0$$

Subtract 211600 from 40000 to get -171600.

$$x^{2}-171600=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -171600 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-171600\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-171600\right)}}{2}$$

Multiply -4 times -171600.

$$x=\frac{0±\sqrt{686400}}{2}$$

Take the square root of 686400.

$$x=\frac{0±40\sqrt{429}}{2}$$

Now solve the equation x=\frac{0±40\sqrt{429}}{2} when ± is plus.

$$x=20\sqrt{429}$$

Now solve the equation x=\frac{0±40\sqrt{429}}{2} when ± is minus.

$$x=-20\sqrt{429}$$

The equation is now solved.

$$x=20\sqrt{429} x=-20\sqrt{429}$$