Solve 3x^2+125/9=0

$$3 { x }^{ 2 } + \frac{ 125 }{ 9 } =0$$

Solve for x (complex solution)

$$x=-\frac{5\sqrt{15}i}{9}\approx -0-2.151657415i$$

$$x=\frac{5\sqrt{15}i}{9}\approx 2.151657415i$$

Steps by Finding Square Root

Subtract \frac{125}{9} from both sides. Anything subtracted from zero gives its negation.

$$3x^{2}=-\frac{125}{9}$$

Divide both sides by 3.

$$x^{2}=\frac{-\frac{125}{9}}{3}$$

Express \frac{-\frac{125}{9}}{3} as a single fraction.

$$x^{2}=\frac{-125}{9\times 3}$$

Multiply 9 and 3 to get 27.

$$x^{2}=\frac{-125}{27}$$

Fraction \frac{-125}{27} can be rewritten as -\frac{125}{27} by extracting the negative sign.

$$x^{2}=-\frac{125}{27}$$

The equation is now solved.

$$x=\frac{5\sqrt{15}i}{9} x=-\frac{5\sqrt{15}i}{9}$$

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.

$$3x^{2}+\frac{125}{9}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and \frac{125}{9} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times \frac{125}{9}}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\times \frac{125}{9}}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\times \frac{125}{9}}}{2\times 3}$$

Multiply -12 times \frac{125}{9}.

$$x=\frac{0±\sqrt{-\frac{500}{3}}}{2\times 3}$$

Take the square root of -\frac{500}{3}.

$$x=\frac{0±\frac{10\sqrt{15}i}{3}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±\frac{10\sqrt{15}i}{3}}{6}$$

Now solve the equation x=\frac{0±\frac{10\sqrt{15}i}{3}}{6} when ± is plus.

$$x=\frac{5\sqrt{15}i}{9}$$

Now solve the equation x=\frac{0±\frac{10\sqrt{15}i}{3}}{6} when ± is minus.

$$x=-\frac{5\sqrt{15}i}{9}$$

The equation is now solved.

$$x=\frac{5\sqrt{15}i}{9} x=-\frac{5\sqrt{15}i}{9}$$