Solve -x(5x+2)=3x^2

$$- x ( 5 x + 2 ) = 3 x ^ { 2 }$$

Solve for x

$$x=-\frac{1}{4}=-0.25$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply -x by 5x+2.

$$5\left(-x\right)x+2\left(-x\right)=3x^{2}$$

Subtract 3x^{2} from both sides.

$$5\left(-x\right)x+2\left(-x\right)-3x^{2}=0$$

Multiply 5 and -1 to get -5.

$$-5xx+2\left(-1\right)x-3x^{2}=0$$

Multiply x and x to get x^{2}.

$$-5x^{2}+2\left(-1\right)x-3x^{2}=0$$

Multiply 2 and -1 to get -2.

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

Combine -5x^{2} and -3x^{2} to get -8x^{2}.

$$-8x^{2}-2x=0$$

Factor out x.

$$x\left(-8x-2\right)=0$$

To find equation solutions, solve x=0 and -8x-2=0.

$$x=0 x=-\frac{1}{4}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply -x by 5x+2.

$$5\left(-x\right)x+2\left(-x\right)=3x^{2}$$

Subtract 3x^{2} from both sides.

$$5\left(-x\right)x+2\left(-x\right)-3x^{2}=0$$

Multiply 5 and -1 to get -5.

$$-5xx+2\left(-1\right)x-3x^{2}=0$$

Multiply x and x to get x^{2}.

$$-5x^{2}+2\left(-1\right)x-3x^{2}=0$$

Multiply 2 and -1 to get -2.

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

Combine -5x^{2} and -3x^{2} to get -8x^{2}.

$$-8x^{2}-2x=0$$

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

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}}}{2\left(-8\right)}$$

Take the square root of \left(-2\right)^{2}.

$$x=\frac{-\left(-2\right)±2}{2\left(-8\right)}$$

The opposite of -2 is 2.

$$x=\frac{2±2}{2\left(-8\right)}$$

Multiply 2 times -8.

$$x=\frac{2±2}{-16}$$

Now solve the equation x=\frac{2±2}{-16} when ± is plus. Add 2 to 2.

$$x=\frac{4}{-16}$$

Reduce the fraction \frac{4}{-16} to lowest terms by extracting and canceling out 4.

$$x=-\frac{1}{4}$$

Now solve the equation x=\frac{2±2}{-16} when ± is minus. Subtract 2 from 2.

$$x=\frac{0}{-16}$$

Divide 0 by -16.

$$x=0$$

The equation is now solved.

$$x=-\frac{1}{4} x=0$$

Steps for Completing the Square

Use the distributive property to multiply -x by 5x+2.

$$5\left(-x\right)x+2\left(-x\right)=3x^{2}$$

Subtract 3x^{2} from both sides.

$$5\left(-x\right)x+2\left(-x\right)-3x^{2}=0$$

Multiply 5 and -1 to get -5.

$$-5xx+2\left(-1\right)x-3x^{2}=0$$

Multiply x and x to get x^{2}.

$$-5x^{2}+2\left(-1\right)x-3x^{2}=0$$

Multiply 2 and -1 to get -2.

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

Combine -5x^{2} and -3x^{2} to get -8x^{2}.

$$-8x^{2}-2x=0$$

Divide both sides by -8.

$$\frac{-8x^{2}-2x}{-8}=\frac{0}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$x^{2}+\left(-\frac{2}{-8}\right)x=\frac{0}{-8}$$

Reduce the fraction \frac{-2}{-8} to lowest terms by extracting and canceling out 2.

$$x^{2}+\frac{1}{4}x=\frac{0}{-8}$$

Divide 0 by -8.

$$x^{2}+\frac{1}{4}x=0$$

Divide \frac{1}{4}, the coefficient of the x term, by 2 to get \frac{1}{8}. Then add the square of \frac{1}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{1}{4}x+\left(\frac{1}{8}\right)^{2}=\left(\frac{1}{8}\right)^{2}$$

Square \frac{1}{8} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{1}{4}x+\frac{1}{64}=\frac{1}{64}$$

Factor x^{2}+\frac{1}{4}x+\frac{1}{64}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1}{8}\right)^{2}=\frac{1}{64}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1}{8}\right)^{2}}=\sqrt{\frac{1}{64}}$$

Simplify.

$$x+\frac{1}{8}=\frac{1}{8} x+\frac{1}{8}=-\frac{1}{8}$$

Subtract \frac{1}{8} from both sides of the equation.

$$x=0 x=-\frac{1}{4}$$