Solve Using the Quadratic Formula (x-3)(x+5)=9

$(x - 3) (x + 5) = 9$

Step 1

Move all terms to the left side of the equation and simplify.

Simplify the left side.

Simplify $(x - 3) (x + 5)$ .

Expand $(x - 3) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$x (x + 5) - 3 (x + 5) = 9$

Apply the distributive property.

$x \cdot x + x \cdot 5 - 3 (x + 5) = 9$

Apply the distributive property.

$x \cdot x + x \cdot 5 - 3 x - 3 \cdot 5 = 9$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 5 - 3 x - 3 \cdot 5 = 9$

Move $5$ to the left of $x$ .

$x^{2} + 5 \cdot x - 3 x - 3 \cdot 5 = 9$

Multiply $- 3$ by $5$ .

$x^{2} + 5 x - 3 x - 15 = 9$

Subtract $3 x$ from $5 x$ .

$x^{2} + 2 x - 15 = 9$

Subtract $9$ from both sides of the equation.

$x^{2} + 2 x - 15 - 9 = 0$

Subtract $9$ from $- 15$ .

$x^{2} + 2 x - 24 = 0$

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 $a = 1$ , $b = 2$ , and $c = - 24$ into the quadratic formula and solve for $x$ .

$\frac{- 2 \pm \sqrt{2^{2} - 4 \cdot (1 \cdot - 24)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot 1 \cdot - 24}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 24$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot - 24}}{2 \cdot 1}$

Multiply $- 4$ by $- 24$ .

$x = \frac{- 2 \pm \sqrt{4 + 96}}{2 \cdot 1}$

Add $4$ and $96$ .

$x = \frac{- 2 \pm \sqrt{100}}{2 \cdot 1}$

Rewrite $100$ as $10^{2}$ .

$x = \frac{- 2 \pm \sqrt{10^{2}}}{2 \cdot 1}$

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

$x = \frac{- 2 \pm 10}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 2 \pm 10}{2}$

Simplify $\frac{- 2 \pm 10}{2}$ .

$x = - 1 \pm 5$

Step 5

The final answer is the combination of both solutions.

$x = 4, - 6$

Solve Using the Quadratic Formula (x-3)(x+5)=9

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