Solve X^2+9=0

$$X ^ { 2 } + 9 = 0$$

Solve for X

$$X=-3i$$

$$X=3i$$

Steps by Finding Square Root

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$X^{2}=-9$$

The equation is now solved.

$$X=3i X=-3i$$

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.

$$X^{2}+9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$X=\frac{0±\sqrt{0^{2}-4\times 9}}{2}$$

Square 0.

$$X=\frac{0±\sqrt{-4\times 9}}{2}$$

Multiply -4 times 9.

$$X=\frac{0±\sqrt{-36}}{2}$$

Take the square root of -36.

$$X=\frac{0±6i}{2}$$

Now solve the equation X=\frac{0±6i}{2} when ± is plus.

$$X=3i$$

Now solve the equation X=\frac{0±6i}{2} when ± is minus.

$$X=-3i$$

The equation is now solved.

$$X=3i X=-3i$$