Solve 6371.634^2=6371^2+x^2

$${ 6371.634 }^{ 2 } = { 6371 }^{ 2 } + { x }^{ 2 }$$

Solve for x

$$x = \frac{\sqrt{2019707489}}{500} \approx 89.882311697$$

$$x = -\frac{\sqrt{2019707489}}{500} \approx -89.882311697$$

Steps by Finding Square Root

Calculate 6371.634 to the power of 2 and get 40597719.829956.

$$40597719.829956=6371^{2}+x^{2}$$

Calculate 6371 to the power of 2 and get 40589641.

$$40597719.829956=40589641+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$40589641+x^{2}=40597719.829956$$

Subtract 40589641 from both sides.

$$x^{2}=40597719.829956-40589641$$

Subtract 40589641 from 40597719.829956 to get 8078.829956.

$$x^{2}=8078.829956$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{2019707489}}{500} x=-\frac{\sqrt{2019707489}}{500}$$

Steps Using the Quadratic Formula

Calculate 6371.634 to the power of 2 and get 40597719.829956.

$$40597719.829956=6371^{2}+x^{2}$$

Calculate 6371 to the power of 2 and get 40589641.

$$40597719.829956=40589641+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$40589641+x^{2}=40597719.829956$$

Subtract 40597719.829956 from both sides.

$$40589641+x^{2}-40597719.829956=0$$

Subtract 40597719.829956 from 40589641 to get -8078.829956.

$$-8078.829956+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-8078.829956=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -8078.829956 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-8078.829956\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-8078.829956\right)}}{2}$$

Multiply -4 times -8078.829956.

$$x=\frac{0±\sqrt{32315.319824}}{2}$$

Take the square root of 32315.319824.

$$x=\frac{0±\frac{\sqrt{2019707489}}{250}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{2019707489}}{250}}{2} when ± is plus.

$$x=\frac{\sqrt{2019707489}}{500}$$

Now solve the equation x=\frac{0±\frac{\sqrt{2019707489}}{250}}{2} when ± is minus.

$$x=-\frac{\sqrt{2019707489}}{500}$$

The equation is now solved.

$$x=\frac{\sqrt{2019707489}}{500} x=-\frac{\sqrt{2019707489}}{500}$$