Solve x^2+0.07x-.026=0

$$x ^ { 2 } + 0.07 x - .026 = 0$$

Solve for x

$$x=0.13$$

$$x=-0.2$$

Steps Using the Quadratic Formula

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x^{2}+0.07x-0.026=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0.07 for b, and -0.026 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-0.07±\sqrt{0.07^{2}-4\left(-0.026\right)}}{2}$$

Square 0.07 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-0.07±\sqrt{0.0049-4\left(-0.026\right)}}{2}$$

Multiply -4 times -0.026.

$$x=\frac{-0.07±\sqrt{0.0049+0.104}}{2}$$

Add 0.0049 to 0.104 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-0.07±\sqrt{0.1089}}{2}$$

Take the square root of 0.1089.

$$x=\frac{-0.07±\frac{33}{100}}{2}$$

Now solve the equation x=\frac{-0.07±\frac{33}{100}}{2} when ± is plus. Add -0.07 to \frac{33}{100} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{13}{50}}{2}$$

Divide \frac{13}{50} by 2.

$$x=\frac{13}{100}$$

Now solve the equation x=\frac{-0.07±\frac{33}{100}}{2} when ± is minus. Subtract \frac{33}{100} from -0.07 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{2}{5}}{2}$$

Divide -\frac{2}{5} by 2.

$$x=-\frac{1}{5}$$

The equation is now solved.

$$x=\frac{13}{100} x=-\frac{1}{5}$$

Steps for Completing the Square

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$x^{2}+0.07x-0.026=0$$

Add 0.026 to both sides of the equation.

$$x^{2}+0.07x-0.026-\left(-0.026\right)=-\left(-0.026\right)$$

Subtracting -0.026 from itself leaves 0.

$$x^{2}+0.07x=-\left(-0.026\right)$$

Subtract -0.026 from 0.

$$x^{2}+0.07x=0.026$$

Divide 0.07, the coefficient of the x term, by 2 to get 0.035. Then add the square of 0.035 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+0.07x+0.035^{2}=0.026+0.035^{2}$$

Square 0.035 by squaring both the numerator and the denominator of the fraction.

$$x^{2}+0.07x+0.001225=0.026+0.001225$$

Add 0.026 to 0.001225 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+0.07x+0.001225=0.027225$$

Factor x^{2}+0.07x+0.001225. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+0.035\right)^{2}=0.027225$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+0.035\right)^{2}}=\sqrt{0.027225}$$

Simplify.

$$x+0.035=\frac{33}{200} x+0.035=-\frac{33}{200}$$

Subtract 0.035 from both sides of the equation.

$$x=\frac{13}{100} x=-\frac{1}{5}$$