Solve 6371634^2=6371^2+x^2

$${ 6371634 }^{ 2 } = { 6371 }^{ 2 } + { x }^{ 2 }$$

Solve for x

$$x=\sqrt{40597679240315}\approx 6371630.814816172$$

$$x=-\sqrt{40597679240315}\approx -6371630.814816172$$

Steps by Finding Square Root

Calculate 6371634 to the power of 2 and get 40597719829956.

$$40597719829956=6371^{2}+x^{2}$$

Calculate 6371 to the power of 2 and get 40589641.

$$40597719829956=40589641+x^{2}$$

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

$$40589641+x^{2}=40597719829956$$

Subtract 40589641 from both sides.

$$x^{2}=40597719829956-40589641$$

Subtract 40589641 from 40597719829956 to get 40597679240315.

$$x^{2}=40597679240315$$

Take the square root of both sides of the equation.

$$x=\sqrt{40597679240315} x=-\sqrt{40597679240315}$$

Steps Using the Quadratic Formula

Calculate 6371634 to the power of 2 and get 40597719829956.

$$40597719829956=6371^{2}+x^{2}$$

Calculate 6371 to the power of 2 and get 40589641.

$$40597719829956=40589641+x^{2}$$

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

$$40589641+x^{2}=40597719829956$$

Subtract 40597719829956 from both sides.

$$40589641+x^{2}-40597719829956=0$$

Subtract 40597719829956 from 40589641 to get -40597679240315.

$$-40597679240315+x^{2}=0$$

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.

$$x^{2}-40597679240315=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -40597679240315 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-40597679240315\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-40597679240315\right)}}{2}$$

Multiply -4 times -40597679240315.

$$x=\frac{0±\sqrt{162390716961260}}{2}$$

Take the square root of 162390716961260.

$$x=\frac{0±2\sqrt{40597679240315}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{40597679240315}}{2} when ± is plus.

$$x=\sqrt{40597679240315}$$

Now solve the equation x=\frac{0±2\sqrt{40597679240315}}{2} when ± is minus.

$$x=-\sqrt{40597679240315}$$

The equation is now solved.

$$x=\sqrt{40597679240315} x=-\sqrt{40597679240315}$$