Solve x^2+102=64

$$x ^ { 2 } + 102 = 64$$

Solve for x (complex solution)

$$x=-\sqrt{38}i\approx -0-6.164414003i$$

$$x=\sqrt{38}i\approx 6.164414003i$$

Steps by Finding Square Root

Subtract 102 from both sides.

$$x^{2}=64-102$$

Subtract 102 from 64 to get -38.

$$x^{2}=-38$$

The equation is now solved.

$$x=\sqrt{38}i x=-\sqrt{38}i$$

Steps Using the Quadratic Formula

Subtract 64 from both sides.

$$x^{2}+102-64=0$$

Subtract 64 from 102 to get 38.

$$x^{2}+38=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 38 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 38}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 38}}{2}$$

Multiply -4 times 38.

$$x=\frac{0±\sqrt{-152}}{2}$$

Take the square root of -152.

$$x=\frac{0±2\sqrt{38}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{38}i}{2} when ± is plus.

$$x=\sqrt{38}i$$

Now solve the equation x=\frac{0±2\sqrt{38}i}{2} when ± is minus.

$$x=-\sqrt{38}i$$

The equation is now solved.

$$x=\sqrt{38}i x=-\sqrt{38}i$$