Solve 8x^2+24x+20x=0

$$8 x ^ { 2 } + 24 x + 20 x = 0$$

Solve for x

$$x = -\frac{11}{2} = -5\frac{1}{2} = -5.5$$

$$x=0$$

Steps Using Factoring

Factor out x.

$$x\left(8x+24+20\right)=0$$

To find equation solutions, solve x=0 and 8x+44=0.

$$x=0 x=-\frac{11}{2}$$

Steps Using the Quadratic Formula

Combine 24x and 20x to get 44x.

$$8x^{2}+44x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 44 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-44±\sqrt{44^{2}}}{2\times 8}$$

Take the square root of 44^{2}.

$$x=\frac{-44±44}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{-44±44}{16}$$

Now solve the equation x=\frac{-44±44}{16} when ± is plus. Add -44 to 44.

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

Divide 0 by 16.

$$x=0$$

Now solve the equation x=\frac{-44±44}{16} when ± is minus. Subtract 44 from -44.

$$x=-\frac{88}{16}$$

Reduce the fraction \frac{-88}{16} to lowest terms by extracting and canceling out 8.

$$x=-\frac{11}{2}$$

The equation is now solved.

$$x=0 x=-\frac{11}{2}$$

Steps for Completing the Square

Combine 24x and 20x to get 44x.

$$8x^{2}+44x=0$$

Divide both sides by 8.

$$\frac{8x^{2}+44x}{8}=\frac{0}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x^{2}+\frac{44}{8}x=\frac{0}{8}$$

Reduce the fraction \frac{44}{8} to lowest terms by extracting and canceling out 4.

$$x^{2}+\frac{11}{2}x=\frac{0}{8}$$

Divide 0 by 8.

$$x^{2}+\frac{11}{2}x=0$$

Divide \frac{11}{2}, the coefficient of the x term, by 2 to get \frac{11}{4}. Then add the square of \frac{11}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{11}{2}x+\left(\frac{11}{4}\right)^{2}=\left(\frac{11}{4}\right)^{2}$$

Square \frac{11}{4} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{11}{2}x+\frac{121}{16}=\frac{121}{16}$$

Factor x^{2}+\frac{11}{2}x+\frac{121}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{11}{4}\right)^{2}=\frac{121}{16}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{11}{4}\right)^{2}}=\sqrt{\frac{121}{16}}$$

Simplify.

$$x+\frac{11}{4}=\frac{11}{4} x+\frac{11}{4}=-\frac{11}{4}$$

Subtract \frac{11}{4} from both sides of the equation.

$$x=0 x=-\frac{11}{2}$$