Solve 9x^2+9=0

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

Solve for x (complex solution)

$$x=-i$$

$$x=i$$

Steps by Finding Square Root

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

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

Divide both sides by 9.

$$x^{2}=\frac{-9}{9}$$

Divide -9 by 9 to get -1.

$$x^{2}=-1$$

The equation is now solved.

$$x=i x=-i$$

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.

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

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

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

Square 0.

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

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\times 9}}{2\times 9}$$

Multiply -36 times 9.

$$x=\frac{0±\sqrt{-324}}{2\times 9}$$

Take the square root of -324.

$$x=\frac{0±18i}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±18i}{18}$$

Now solve the equation x=\frac{0±18i}{18} when ± is plus.

$$x=i$$

Now solve the equation x=\frac{0±18i}{18} when ± is minus.

$$x=-i$$

The equation is now solved.

$$x=i x=-i$$