Solve 30x^2+2x-08=0

$$30 x ^ { 2 } + 2 x - 08 = 0$$

Solve for x

$$x=-\frac{1}{15}\approx -0.066666667$$

$$x=0$$

Steps Using Factoring

Multiply 0 and 8 to get 0.

$$30x^{2}+2x-0=0$$

Reorder the terms.

$$30x^{2}+2x=0$$

Factor out x.

$$x\left(30x+2\right)=0$$

To find equation solutions, solve x=0 and 30x+2=0.

$$x=0 x=-\frac{1}{15}$$

Steps Using the Quadratic Formula

Multiply 0 and 8 to get 0.

$$30x^{2}+2x-0=0$$

Reorder the terms.

$$30x^{2}+2x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 30 for a, 2 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}}}{2\times 30}$$

Take the square root of 2^{2}.

$$x=\frac{-2±2}{2\times 30}$$

Multiply 2 times 30.

$$x=\frac{-2±2}{60}$$

Now solve the equation x=\frac{-2±2}{60} when ± is plus. Add -2 to 2.

$$x=\frac{0}{60}$$

Divide 0 by 60.

$$x=0$$

Now solve the equation x=\frac{-2±2}{60} when ± is minus. Subtract 2 from -2.

$$x=-\frac{4}{60}$$

Reduce the fraction \frac{-4}{60} to lowest terms by extracting and canceling out 4.

$$x=-\frac{1}{15}$$

The equation is now solved.

$$x=0 x=-\frac{1}{15}$$

Steps for Completing the Square

Multiply 0 and 8 to get 0.

$$30x^{2}+2x-0=0$$

Add 0 to both sides.

$$30x^{2}+2x=0+0$$

Add 0 and 0 to get 0.

$$30x^{2}+2x=0$$

Divide both sides by 30.

$$\frac{30x^{2}+2x}{30}=\frac{0}{30}$$

Dividing by 30 undoes the multiplication by 30.

$$x^{2}+\frac{2}{30}x=\frac{0}{30}$$

Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.

$$x^{2}+\frac{1}{15}x=\frac{0}{30}$$

Divide 0 by 30.

$$x^{2}+\frac{1}{15}x=0$$

Divide \frac{1}{15}, the coefficient of the x term, by 2 to get \frac{1}{30}. Then add the square of \frac{1}{30} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{1}{15}x+\left(\frac{1}{30}\right)^{2}=\left(\frac{1}{30}\right)^{2}$$

Square \frac{1}{30} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{1}{15}x+\frac{1}{900}=\frac{1}{900}$$

Factor x^{2}+\frac{1}{15}x+\frac{1}{900}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1}{30}\right)^{2}=\frac{1}{900}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1}{30}\right)^{2}}=\sqrt{\frac{1}{900}}$$

Simplify.

$$x+\frac{1}{30}=\frac{1}{30} x+\frac{1}{30}=-\frac{1}{30}$$

Subtract \frac{1}{30} from both sides of the equation.

$$x=0 x=-\frac{1}{15}$$