Solve 8^2=10^2+x^2

$$8 ^ { 2 } = 10 ^ { 2 } + x ^ { 2 }$$

Solve for x (complex solution)

$$x=-6i$$

$$x=6i$$

Steps by Finding Square Root

Calculate 8 to the power of 2 and get 64.

$$64=10^{2}+x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$64=100+x^{2}$$

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

$$100+x^{2}=64$$

Subtract 100 from both sides.

$$x^{2}=64-100$$

Subtract 100 from 64 to get -36.

$$x^{2}=-36$$

The equation is now solved.

$$x=6i x=-6i$$

Steps Using the Quadratic Formula

Calculate 8 to the power of 2 and get 64.

$$64=10^{2}+x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$64=100+x^{2}$$

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

$$100+x^{2}=64$$

Subtract 64 from both sides.

$$100+x^{2}-64=0$$

Subtract 64 from 100 to get 36.

$$36+x^{2}=0$$

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.

$$x^{2}+36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 36}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 36}}{2}$$

Multiply -4 times 36.

$$x=\frac{0±\sqrt{-144}}{2}$$

Take the square root of -144.

$$x=\frac{0±12i}{2}$$

Now solve the equation x=\frac{0±12i}{2} when ± is plus.

$$x=6i$$

Now solve the equation x=\frac{0±12i}{2} when ± is minus.

$$x=-6i$$

The equation is now solved.

$$x=6i x=-6i$$