Solve d^2-9d

$$d ^ { 2 } - 9 d$$

Factor

$$d\left(d-9\right)$$

Solution Steps

Factor out d.

$$d\left(d-9\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$d^{2}-9d=0$$

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.

$$d=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}}}{2}$$

Take the square root of \left(-9\right)^{2}.

$$d=\frac{-\left(-9\right)±9}{2}$$

The opposite of -9 is 9.

$$d=\frac{9±9}{2}$$

Now solve the equation d=\frac{9±9}{2} when ± is plus. Add 9 to 9.

$$d=\frac{18}{2}$$

Divide 18 by 2.

$$d=9$$

Now solve the equation d=\frac{9±9}{2} when ± is minus. Subtract 9 from 9.

$$d=\frac{0}{2}$$

Divide 0 by 2.

$$d=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 9 for x_{1} and 0 for x_{2}.

$$d^{2}-9d=\left(d-9\right)d$$

Evaluate

$$d\left(d-9\right)$$