Solve 8x^2=-26x

$$8 x ^ { 2 } = - 26 x$$

Solve for x

$$x = -\frac{13}{4} = -3\frac{1}{4} = -3.25$$

$$x=0$$

Steps Using Factoring

Add 26x to both sides.

$$8x^{2}+26x=0$$

Factor out x.

$$x\left(8x+26\right)=0$$

To find equation solutions, solve x=0 and 8x+26=0.

$$x=0 x=-\frac{13}{4}$$

Steps Using the Quadratic Formula

Add 26x to both sides.

$$8x^{2}+26x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 26 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-26±\sqrt{26^{2}}}{2\times 8}$$

Take the square root of 26^{2}.

$$x=\frac{-26±26}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{-26±26}{16}$$

Now solve the equation x=\frac{-26±26}{16} when ± is plus. Add -26 to 26.

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

Divide 0 by 16.

$$x=0$$

Now solve the equation x=\frac{-26±26}{16} when ± is minus. Subtract 26 from -26.

$$x=-\frac{52}{16}$$

Reduce the fraction \frac{-52}{16} to lowest terms by extracting and canceling out 4.

$$x=-\frac{13}{4}$$

The equation is now solved.

$$x=0 x=-\frac{13}{4}$$

Steps for Completing the Square

Add 26x to both sides.

$$8x^{2}+26x=0$$

Divide both sides by 8.

$$\frac{8x^{2}+26x}{8}=\frac{0}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x^{2}+\frac{26}{8}x=\frac{0}{8}$$

Reduce the fraction \frac{26}{8} to lowest terms by extracting and canceling out 2.

$$x^{2}+\frac{13}{4}x=\frac{0}{8}$$

Divide 0 by 8.

$$x^{2}+\frac{13}{4}x=0$$

Divide \frac{13}{4}, the coefficient of the x term, by 2 to get \frac{13}{8}. Then add the square of \frac{13}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{13}{4}x+\left(\frac{13}{8}\right)^{2}=\left(\frac{13}{8}\right)^{2}$$

Square \frac{13}{8} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{13}{4}x+\frac{169}{64}=\frac{169}{64}$$

Factor x^{2}+\frac{13}{4}x+\frac{169}{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}.

$$\left(x+\frac{13}{8}\right)^{2}=\frac{169}{64}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{13}{8}\right)^{2}}=\sqrt{\frac{169}{64}}$$

Simplify.

$$x+\frac{13}{8}=\frac{13}{8} x+\frac{13}{8}=-\frac{13}{8}$$

Subtract \frac{13}{8} from both sides of the equation.

$$x=0 x=-\frac{13}{4}$$