Solve 6371^2-6376^2=x^2

$${ 6371 }^{ 2 } - { 6376 }^{ 2 } = { x }^{ 2 }$$

Solve for x (complex solution)

$$x=-\sqrt{63735}i\approx -0-252.457917285i$$

$$x=\sqrt{63735}i\approx 252.457917285i$$

Steps by Finding Square Root

Calculate 6371 to the power of 2 and get 40589641.

$$40589641-6376^{2}=x^{2}$$

Calculate 6376 to the power of 2 and get 40653376.

$$40589641-40653376=x^{2}$$

Subtract 40653376 from 40589641 to get -63735.

$$-63735=x^{2}$$

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

$$x^{2}=-63735$$

The equation is now solved.

$$x=\sqrt{63735}i x=-\sqrt{63735}i$$

Steps Using the Quadratic Formula

Calculate 6371 to the power of 2 and get 40589641.

$$40589641-6376^{2}=x^{2}$$

Calculate 6376 to the power of 2 and get 40653376.

$$40589641-40653376=x^{2}$$

Subtract 40653376 from 40589641 to get -63735.

$$-63735=x^{2}$$

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

$$x^{2}=-63735$$

Add 63735 to both sides.

$$x^{2}+63735=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 63735 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 63735}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 63735}}{2}$$

Multiply -4 times 63735.

$$x=\frac{0±\sqrt{-254940}}{2}$$

Take the square root of -254940.

$$x=\frac{0±2\sqrt{63735}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{63735}i}{2} when ± is plus.

$$x=\sqrt{63735}i$$

Now solve the equation x=\frac{0±2\sqrt{63735}i}{2} when ± is minus.

$$x=-\sqrt{63735}i$$

The equation is now solved.

$$x=\sqrt{63735}i x=-\sqrt{63735}i$$