Solve 5x^2+6x+x=0=

$$5 { x }^{ 2 } +6x+x=0=$$

Solve for x

$$x = -\frac{7}{5} = -1\frac{2}{5} = -1.4$$

$$x=0$$

Steps Using Factoring

Factor out x.

$$x\left(5x+6+1\right)=0$$

To find equation solutions, solve x=0 and 5x+7=0.

$$x=0 x=-\frac{7}{5}$$

Steps Using the Quadratic Formula

Combine 6x and x to get 7x.

$$5x^{2}+7x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 7 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-7±\sqrt{7^{2}}}{2\times 5}$$

Take the square root of 7^{2}.

$$x=\frac{-7±7}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{-7±7}{10}$$

Now solve the equation x=\frac{-7±7}{10} when ± is plus. Add -7 to 7.

$$x=\frac{0}{10}$$

Divide 0 by 10.

$$x=0$$

Now solve the equation x=\frac{-7±7}{10} when ± is minus. Subtract 7 from -7.

$$x=-\frac{14}{10}$$

Reduce the fraction \frac{-14}{10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{7}{5}$$

The equation is now solved.

$$x=0 x=-\frac{7}{5}$$

Steps for Completing the Square

Combine 6x and x to get 7x.

$$5x^{2}+7x=0$$

Divide both sides by 5.

$$\frac{5x^{2}+7x}{5}=\frac{0}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x^{2}+\frac{7}{5}x=\frac{0}{5}$$

Divide 0 by 5.

$$x^{2}+\frac{7}{5}x=0$$

Divide \frac{7}{5}, the coefficient of the x term, by 2 to get \frac{7}{10}. Then add the square of \frac{7}{10} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{7}{5}x+\left(\frac{7}{10}\right)^{2}=\left(\frac{7}{10}\right)^{2}$$

Square \frac{7}{10} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{7}{5}x+\frac{49}{100}=\frac{49}{100}$$

Factor x^{2}+\frac{7}{5}x+\frac{49}{100}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{7}{10}\right)^{2}=\frac{49}{100}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{7}{10}\right)^{2}}=\sqrt{\frac{49}{100}}$$

Simplify.

$$x+\frac{7}{10}=\frac{7}{10} x+\frac{7}{10}=-\frac{7}{10}$$

Subtract \frac{7}{10} from both sides of the equation.

$$x=0 x=-\frac{7}{5}$$