Solve 0=0.08x^2+1.6x

$$0 = 0.08 { x }^{ 2 } +1.6x$$

Solve for x

$$x=-20$$

$$x=0$$

Steps Using Factoring

Swap sides so that all variable terms are on the left hand side.

$$0.08x^{2}+1.6x=0$$

Factor out x.

$$x\left(0.08x+1.6\right)=0$$

To find equation solutions, solve x=0 and \frac{2x}{25}+1.6=0.

$$x=0 x=-20$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$0.08x^{2}+1.6x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.08 for a, 1.6 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1.6±\sqrt{1.6^{2}}}{2\times 0.08}$$

Take the square root of 1.6^{2}.

$$x=\frac{-1.6±\frac{8}{5}}{2\times 0.08}$$

Multiply 2 times 0.08.

$$x=\frac{-1.6±\frac{8}{5}}{0.16}$$

Now solve the equation x=\frac{-1.6±\frac{8}{5}}{0.16} when ± is plus. Add -1.6 to \frac{8}{5} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0}{0.16}$$

Divide 0 by 0.16 by multiplying 0 by the reciprocal of 0.16.

$$x=0$$

Now solve the equation x=\frac{-1.6±\frac{8}{5}}{0.16} when ± is minus. Subtract \frac{8}{5} from -1.6 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{16}{5}}{0.16}$$

Divide -\frac{16}{5} by 0.16 by multiplying -\frac{16}{5} by the reciprocal of 0.16.

$$x=-20$$

The equation is now solved.

$$x=0 x=-20$$

Steps for Completing the Square

Swap sides so that all variable terms are on the left hand side.

$$0.08x^{2}+1.6x=0$$

Divide both sides of the equation by 0.08, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.08x^{2}+1.6x}{0.08}=\frac{0}{0.08}$$

Dividing by 0.08 undoes the multiplication by 0.08.

$$x^{2}+\frac{1.6}{0.08}x=\frac{0}{0.08}$$

Divide 1.6 by 0.08 by multiplying 1.6 by the reciprocal of 0.08.

$$x^{2}+20x=\frac{0}{0.08}$$

Divide 0 by 0.08 by multiplying 0 by the reciprocal of 0.08.

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

Divide 20, the coefficient of the x term, by 2 to get 10. Then add the square of 10 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+20x+10^{2}=10^{2}$$

Square 10.

$$x^{2}+20x+100=100$$

Factor x^{2}+20x+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}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$x+10=10 x+10=-10$$

Subtract 10 from both sides of the equation.

$$x=0 x=-20$$