Solve 16x^2+9=0

$$16 x ^ { 2 } + 9 = 0$$

Solve for x (complex solution)

$$x=-\frac{3}{4}i=-0.75i$$

$$x=\frac{3}{4}i=0.75i$$

Steps by Finding Square Root

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

$$16x^{2}=-9$$

Divide both sides by 16.

$$x^{2}=-\frac{9}{16}$$

The equation is now solved.

$$x=\frac{3}{4}i x=-\frac{3}{4}i$$

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.

$$16x^{2}+9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 for a, 0 for b, and 9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\times 9}}{2\times 16}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 16\times 9}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{0±\sqrt{-64\times 9}}{2\times 16}$$

Multiply -64 times 9.

$$x=\frac{0±\sqrt{-576}}{2\times 16}$$

Take the square root of -576.

$$x=\frac{0±24i}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{0±24i}{32}$$

Now solve the equation x=\frac{0±24i}{32} when ± is plus.

$$x=\frac{3}{4}i$$

Now solve the equation x=\frac{0±24i}{32} when ± is minus.

$$x=-\frac{3}{4}i$$

The equation is now solved.

$$x=\frac{3}{4}i x=-\frac{3}{4}i$$