Solve 16=d-0.01d^2

$$16 = d - 0.01 d ^ { 2 }$$

Solve for d

$$d=20$$

$$d=80$$

Steps Using the Quadratic Formula

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

$$d-0.01d^{2}=16$$

Subtract 16 from both sides.

$$d-0.01d^{2}-16=0$$

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.

$$-0.01d^{2}+d-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -0.01 for a, 1 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{-1±\sqrt{1^{2}-4\left(-0.01\right)\left(-16\right)}}{2\left(-0.01\right)}$$

Square 1.

$$d=\frac{-1±\sqrt{1-4\left(-0.01\right)\left(-16\right)}}{2\left(-0.01\right)}$$

Multiply -4 times -0.01.

$$d=\frac{-1±\sqrt{1+0.04\left(-16\right)}}{2\left(-0.01\right)}$$

Multiply 0.04 times -16.

$$d=\frac{-1±\sqrt{1-0.64}}{2\left(-0.01\right)}$$

Add 1 to -0.64.

$$d=\frac{-1±\sqrt{0.36}}{2\left(-0.01\right)}$$

Take the square root of 0.36.

$$d=\frac{-1±\frac{3}{5}}{2\left(-0.01\right)}$$

Multiply 2 times -0.01.

$$d=\frac{-1±\frac{3}{5}}{-0.02}$$

Now solve the equation d=\frac{-1±\frac{3}{5}}{-0.02} when ± is plus. Add -1 to \frac{3}{5}.

$$d=-\frac{\frac{2}{5}}{-0.02}$$

Divide -\frac{2}{5} by -0.02 by multiplying -\frac{2}{5} by the reciprocal of -0.02.

$$d=20$$

Now solve the equation d=\frac{-1±\frac{3}{5}}{-0.02} when ± is minus. Subtract \frac{3}{5} from -1.

$$d=-\frac{\frac{8}{5}}{-0.02}$$

Divide -\frac{8}{5} by -0.02 by multiplying -\frac{8}{5} by the reciprocal of -0.02.

$$d=80$$

The equation is now solved.

$$d=20 d=80$$

Steps for Completing the Square

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

$$d-0.01d^{2}=16$$

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.

$$-0.01d^{2}+d=16$$

Multiply both sides by -100.

$$\frac{-0.01d^{2}+d}{-0.01}=\frac{16}{-0.01}$$

Dividing by -0.01 undoes the multiplication by -0.01.

$$d^{2}+\frac{1}{-0.01}d=\frac{16}{-0.01}$$

Divide 1 by -0.01 by multiplying 1 by the reciprocal of -0.01.

$$d^{2}-100d=\frac{16}{-0.01}$$

Divide 16 by -0.01 by multiplying 16 by the reciprocal of -0.01.

$$d^{2}-100d=-1600$$

Divide -100, the coefficient of the x term, by 2 to get -50. Then add the square of -50 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$d^{2}-100d+\left(-50\right)^{2}=-1600+\left(-50\right)^{2}$$

Square -50.

$$d^{2}-100d+2500=-1600+2500$$

Add -1600 to 2500.

$$d^{2}-100d+2500=900$$

Factor d^{2}-100d+2500. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(d-50\right)^{2}=900$$

Take the square root of both sides of the equation.

$$\sqrt{\left(d-50\right)^{2}}=\sqrt{900}$$

Simplify.

$$d-50=30 d-50=-30$$

Add 50 to both sides of the equation.

$$d=80 d=20$$