Solve y^2+64=0

$$y ^ { 2 } + 64 = 0$$

Solve for y

$$y=-8i$$

$$y=8i$$

Steps by Finding Square Root

Subtract 64 from both sides. Anything subtracted from zero gives its negation.

$$y^{2}=-64$$

The equation is now solved.

$$y=8i y=-8i$$

Steps Using the Quadratic Formula

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.

$$y^{2}+64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 64}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 64}}{2}$$

Multiply -4 times 64.

$$y=\frac{0±\sqrt{-256}}{2}$$

Take the square root of -256.

$$y=\frac{0±16i}{2}$$

Now solve the equation y=\frac{0±16i}{2} when ± is plus.

$$y=8i$$

Now solve the equation y=\frac{0±16i}{2} when ± is minus.

$$y=-8i$$

The equation is now solved.

$$y=8i y=-8i$$