Solve (x-9)(x)=0

$$(x-9)(x)=0$$

Solve for x

$$x=0$$

$$x=9$$

Steps Using Factoring

Use the distributive property to multiply x-9 by x.

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

Factor out x.

$$x\left(x-9\right)=0$$

To find equation solutions, solve x=0 and x-9=0.

$$x=0 x=9$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-9 by x.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -9 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

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

$$x=\frac{-\left(-9\right)±9}{2}$$

The opposite of -9 is 9.

$$x=\frac{9±9}{2}$$

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

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

Divide 18 by 2.

$$x=9$$

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

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

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=9 x=0$$

Steps for Completing the Square

Use the distributive property to multiply x-9 by x.

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

Divide -9, the coefficient of the x term, by 2 to get -\frac{9}{2}. Then add the square of -\frac{9}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-9x+\left(-\frac{9}{2}\right)^{2}=\left(-\frac{9}{2}\right)^{2}$$

Square -\frac{9}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-9x+\frac{81}{4}=\frac{81}{4}$$

Factor x^{2}-9x+\frac{81}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{9}{2}\right)^{2}=\frac{81}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{9}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Simplify.

$$x-\frac{9}{2}=\frac{9}{2} x-\frac{9}{2}=-\frac{9}{2}$$

Add \frac{9}{2} to both sides of the equation.

$$x=9 x=0$$