Solve x^2+1.6*10^-2x-1.6*10^-2=0

$$x ^ { 2 } + 1.6 \times 10 ^ { - 2 } x - 1.6 \times 10 ^ { - 2 } = 0$$

Solve for x

$$x=\frac{\sqrt{251}-1}{125}\approx 0.118743836$$

$$x=\frac{-\sqrt{251}-1}{125}\approx -0.134743836$$

Steps Using the Quadratic Formula

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$x^{2}+1.6\times \frac{1}{100}x-1.6\times 10^{-2}=0$$

Multiply 1.6 and \frac{1}{100} to get \frac{2}{125}.

$$x^{2}+\frac{2}{125}x-1.6\times 10^{-2}=0$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$x^{2}+\frac{2}{125}x-1.6\times \frac{1}{100}=0$$

Multiply 1.6 and \frac{1}{100} to get \frac{2}{125}.

$$x^{2}+\frac{2}{125}x-\frac{2}{125}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, \frac{2}{125} for b, and -\frac{2}{125} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{2}{125}±\sqrt{\left(\frac{2}{125}\right)^{2}-4\left(-\frac{2}{125}\right)}}{2}$$

Square \frac{2}{125} by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\frac{2}{125}±\sqrt{\frac{4}{15625}-4\left(-\frac{2}{125}\right)}}{2}$$

Multiply -4 times -\frac{2}{125}.

$$x=\frac{-\frac{2}{125}±\sqrt{\frac{4}{15625}+\frac{8}{125}}}{2}$$

Add \frac{4}{15625} to \frac{8}{125} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\frac{2}{125}±\sqrt{\frac{1004}{15625}}}{2}$$

Take the square root of \frac{1004}{15625}.

$$x=\frac{-\frac{2}{125}±\frac{2\sqrt{251}}{125}}{2}$$

Now solve the equation x=\frac{-\frac{2}{125}±\frac{2\sqrt{251}}{125}}{2} when ± is plus. Add -\frac{2}{125} to \frac{2\sqrt{251}}{125}.

$$x=\frac{2\sqrt{251}-2}{2\times 125}$$

Divide \frac{-2+2\sqrt{251}}{125} by 2.

$$x=\frac{\sqrt{251}-1}{125}$$

Now solve the equation x=\frac{-\frac{2}{125}±\frac{2\sqrt{251}}{125}}{2} when ± is minus. Subtract \frac{2\sqrt{251}}{125} from -\frac{2}{125}.

$$x=\frac{-2\sqrt{251}-2}{2\times 125}$$

Divide \frac{-2-2\sqrt{251}}{125} by 2.

$$x=\frac{-\sqrt{251}-1}{125}$$

The equation is now solved.

$$x=\frac{\sqrt{251}-1}{125} x=\frac{-\sqrt{251}-1}{125}$$

Steps for Completing the Square

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$x^{2}+1.6\times \frac{1}{100}x-1.6\times 10^{-2}=0$$

Multiply 1.6 and \frac{1}{100} to get \frac{2}{125}.

$$x^{2}+\frac{2}{125}x-1.6\times 10^{-2}=0$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$x^{2}+\frac{2}{125}x-1.6\times \frac{1}{100}=0$$

Multiply 1.6 and \frac{1}{100} to get \frac{2}{125}.

$$x^{2}+\frac{2}{125}x-\frac{2}{125}=0$$

Add \frac{2}{125} to both sides. Anything plus zero gives itself.

$$x^{2}+\frac{2}{125}x=\frac{2}{125}$$

Divide \frac{2}{125}, the coefficient of the x term, by 2 to get \frac{1}{125}. Then add the square of \frac{1}{125} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{2}{125}x+\left(\frac{1}{125}\right)^{2}=\frac{2}{125}+\left(\frac{1}{125}\right)^{2}$$

Square \frac{1}{125} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{2}{125}x+\frac{1}{15625}=\frac{2}{125}+\frac{1}{15625}$$

Add \frac{2}{125} to \frac{1}{15625} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{2}{125}x+\frac{1}{15625}=\frac{251}{15625}$$

Factor x^{2}+\frac{2}{125}x+\frac{1}{15625}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1}{125}\right)^{2}=\frac{251}{15625}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1}{125}\right)^{2}}=\sqrt{\frac{251}{15625}}$$

Simplify.

$$x+\frac{1}{125}=\frac{\sqrt{251}}{125} x+\frac{1}{125}=-\frac{\sqrt{251}}{125}$$

Subtract \frac{1}{125} from both sides of the equation.

$$x=\frac{\sqrt{251}-1}{125} x=\frac{-\sqrt{251}-1}{125}$$