Solve 9x^2+5=3

$$9 x ^ { 2 } + 5 = 3$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2}i}{3}\approx -0-0.471404521i$$

$$x=\frac{\sqrt{2}i}{3}\approx 0.471404521i$$

Steps by Finding Square Root

Subtract 5 from both sides.

$$9x^{2}=3-5$$

Subtract 5 from 3 to get -2.

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

Divide both sides by 9.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

Subtract 3 from both sides.

$$9x^{2}+5-3=0$$

Subtract 3 from 5 to get 2.

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

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

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

Square 0.

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

Multiply -4 times 9.

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

Multiply -36 times 2.

$$x=\frac{0±\sqrt{-72}}{2\times 9}$$

Take the square root of -72.

$$x=\frac{0±6\sqrt{2}i}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±6\sqrt{2}i}{18}$$

Now solve the equation x=\frac{0±6\sqrt{2}i}{18} when ± is plus.

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

Now solve the equation x=\frac{0±6\sqrt{2}i}{18} when ± is minus.

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

The equation is now solved.

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