Solve 9x^2+25=0

$$9 { x }^{ 2 } +25 = 0$$

Solve for x (complex solution)

$$x=-\frac{5}{3}i\approx -1.666666667i$$

$$x=\frac{5}{3}i\approx 1.666666667i$$

Steps by Finding Square Root

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$9x^{2}=-25$$

Divide both sides by 9.

$$x^{2}=-\frac{25}{9}$$

The equation is now solved.

$$x=\frac{5}{3}i x=-\frac{5}{3}i$$

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.

$$9x^{2}+25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and 25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\times 25}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\times 25}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\times 25}}{2\times 9}$$

Multiply -36 times 25.

$$x=\frac{0±\sqrt{-900}}{2\times 9}$$

Take the square root of -900.

$$x=\frac{0±30i}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±30i}{18}$$

Now solve the equation x=\frac{0±30i}{18} when ± is plus.

$$x=\frac{5}{3}i$$

Now solve the equation x=\frac{0±30i}{18} when ± is minus.

$$x=-\frac{5}{3}i$$

The equation is now solved.

$$x=\frac{5}{3}i x=-\frac{5}{3}i$$