Solve Using the Quadratic Formula X(X-9)=0

$X (X - 9) = 0$

Step 1

Simplify the left side.

Simplify $X (X - 9)$ .

Apply the distributive property.

$X \cdot X + X \cdot - 9 = 0$

Simplify the expression.

Multiply $X$ by $X$ .

$X^{2} + X \cdot - 9 = 0$

Move $- 9$ to the left of $X$ .

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

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = - 9$ , and $c = 0$ into the quadratic formula and solve for $X$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (1 \cdot 0)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 9$ to the power of $2$ .

$X = \frac{9 \pm \sqrt{81 - 4 \cdot 1 \cdot 0}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 0$ .

Multiply $- 4$ by $1$ .

$X = \frac{9 \pm \sqrt{81 - 4 \cdot 0}}{2 \cdot 1}$

Multiply $- 4$ by $0$ .

$X = \frac{9 \pm \sqrt{81 + 0}}{2 \cdot 1}$

Add $81$ and $0$ .

$X = \frac{9 \pm \sqrt{81}}{2 \cdot 1}$

Rewrite $81$ as $9^{2}$ .

$X = \frac{9 \pm \sqrt{9^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$X = \frac{9 \pm 9}{2 \cdot 1}$

Multiply $2$ by $1$ .

$X = \frac{9 \pm 9}{2}$

Step 5

The final answer is the combination of both solutions.

$X = 9, 0$