Solve 8x^2+9=0

$$8 x ^ { 2 } + 9 = 0$$

Solve for x (complex solution)

$$x=-\frac{3\sqrt{2}i}{4}\approx -0-1.060660172i$$

$$x=\frac{3\sqrt{2}i}{4}\approx 1.060660172i$$

Steps by Finding Square Root

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

$$8x^{2}=-9$$

Divide both sides by 8.

$$x^{2}=-\frac{9}{8}$$

The equation is now solved.

$$x=\frac{3\sqrt{2}i}{4} x=-\frac{3\sqrt{2}i}{4}$$

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.

$$8x^{2}+9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and 9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\times 9}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\times 9}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\times 9}}{2\times 8}$$

Multiply -32 times 9.

$$x=\frac{0±\sqrt{-288}}{2\times 8}$$

Take the square root of -288.

$$x=\frac{0±12\sqrt{2}i}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±12\sqrt{2}i}{16}$$

Now solve the equation x=\frac{0±12\sqrt{2}i}{16} when ± is plus.

$$x=\frac{3\sqrt{2}i}{4}$$

Now solve the equation x=\frac{0±12\sqrt{2}i}{16} when ± is minus.

$$x=-\frac{3\sqrt{2}i}{4}$$

The equation is now solved.

$$x=\frac{3\sqrt{2}i}{4} x=-\frac{3\sqrt{2}i}{4}$$