Solve 132=.005x^2-.03x+121

$$132=.005 { x }^{ 2 } -.03x+121$$

Solve for x

$$x=-44$$

$$x=50$$

Steps Using the Quadratic Formula

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

$$0.005x^{2}-0.03x+121=132$$

Subtract 132 from both sides.

$$0.005x^{2}-0.03x+121-132=0$$

Subtract 132 from 121 to get -11.

$$0.005x^{2}-0.03x-11=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.005 for a, -0.03 for b, and -11 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-0.03\right)±\sqrt{\left(-0.03\right)^{2}-4\times 0.005\left(-11\right)}}{2\times 0.005}$$

Square -0.03 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\left(-0.03\right)±\sqrt{0.0009-4\times 0.005\left(-11\right)}}{2\times 0.005}$$

Multiply -4 times 0.005.

$$x=\frac{-\left(-0.03\right)±\sqrt{0.0009-0.02\left(-11\right)}}{2\times 0.005}$$

Multiply -0.02 times -11.

$$x=\frac{-\left(-0.03\right)±\sqrt{0.0009+0.22}}{2\times 0.005}$$

Add 0.0009 to 0.22 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-0.03\right)±\sqrt{0.2209}}{2\times 0.005}$$

Take the square root of 0.2209.

$$x=\frac{-\left(-0.03\right)±\frac{47}{100}}{2\times 0.005}$$

The opposite of -0.03 is 0.03.

$$x=\frac{0.03±\frac{47}{100}}{2\times 0.005}$$

Multiply 2 times 0.005.

$$x=\frac{0.03±\frac{47}{100}}{0.01}$$

Now solve the equation x=\frac{0.03±\frac{47}{100}}{0.01} when ± is plus. Add 0.03 to \frac{47}{100} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{1}{2}}{0.01}$$

Divide \frac{1}{2} by 0.01 by multiplying \frac{1}{2} by the reciprocal of 0.01.

$$x=50$$

Now solve the equation x=\frac{0.03±\frac{47}{100}}{0.01} when ± is minus. Subtract \frac{47}{100} from 0.03 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{11}{25}}{0.01}$$

Divide -\frac{11}{25} by 0.01 by multiplying -\frac{11}{25} by the reciprocal of 0.01.

$$x=-44$$

The equation is now solved.

$$x=50 x=-44$$

Steps for Completing the Square

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

$$0.005x^{2}-0.03x+121=132$$

Subtract 121 from both sides.

$$0.005x^{2}-0.03x=132-121$$

Subtract 121 from 132 to get 11.

$$0.005x^{2}-0.03x=11$$

Multiply both sides by 200.

$$\frac{0.005x^{2}-0.03x}{0.005}=\frac{11}{0.005}$$

Dividing by 0.005 undoes the multiplication by 0.005.

$$x^{2}+\left(-\frac{0.03}{0.005}\right)x=\frac{11}{0.005}$$

Divide -0.03 by 0.005 by multiplying -0.03 by the reciprocal of 0.005.

$$x^{2}-6x=\frac{11}{0.005}$$

Divide 11 by 0.005 by multiplying 11 by the reciprocal of 0.005.

$$x^{2}-6x=2200$$

Divide -6, the coefficient of the x term, by 2 to get -3. Then add the square of -3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-6x+\left(-3\right)^{2}=2200+\left(-3\right)^{2}$$

Square -3.

$$x^{2}-6x+9=2200+9$$

Add 2200 to 9.

$$x^{2}-6x+9=2209$$

Factor x^{2}-6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-3\right)^{2}=2209$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{2209}$$

Simplify.

$$x-3=47 x-3=-47$$

Add 3 to both sides of the equation.

$$x=50 x=-44$$