Solve Using the Quadratic Formula (x-5)(x+9)=0

$(x - 5) (x + 9) = 0$

Step 1

Simplify the left side.

Simplify $(x - 5) (x + 9)$ .

Expand $(x - 5) (x + 9)$ using the FOIL Method.

Apply the distributive property.

$x (x + 9) - 5 (x + 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 9 - 5 (x + 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 9 - 5 x - 5 \cdot 9 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 9 - 5 x - 5 \cdot 9 = 0$

Move $9$ to the left of $x$ .

$x^{2} + 9 \cdot x - 5 x - 5 \cdot 9 = 0$

Multiply $- 5$ by $9$ .

$x^{2} + 9 x - 5 x - 45 = 0$

Subtract $5 x$ from $9 x$ .

$x^{2} + 4 x - 45 = 0$

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 $a = 1$ , $b = 4$ , and $c = - 45$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (1 \cdot - 45)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 1 \cdot - 45}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 45$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 45}}{2 \cdot 1}$

Multiply $- 4$ by $- 45$ .

$x = \frac{- 4 \pm \sqrt{16 + 180}}{2 \cdot 1}$

Add $16$ and $180$ .

$x = \frac{- 4 \pm \sqrt{196}}{2 \cdot 1}$

Rewrite $196$ as $14^{2}$ .

$x = \frac{- 4 \pm \sqrt{14^{2}}}{2 \cdot 1}$

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

$x = \frac{- 4 \pm 14}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 4 \pm 14}{2}$

Simplify $\frac{- 4 \pm 14}{2}$ .

$x = - 2 \pm 7$

Step 5

The final answer is the combination of both solutions.

$x = 5, - 9$

Solve Using the Quadratic Formula (x-5)(x+9)=0

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