Solve Using the Quadratic Formula (x-5)(x+3)=0

$(x - 5) (x + 3) = 0$

Step 1

Simplify the left side.

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

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

Apply the distributive property.

$x (x + 3) - 5 (x + 3) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 3 - 5 (x + 3) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 3 - 5 x - 5 \cdot 3 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 3 - 5 x - 5 \cdot 3 = 0$

Move $3$ to the left of $x$ .

$x^{2} + 3 \cdot x - 5 x - 5 \cdot 3 = 0$

Multiply $- 5$ by $3$ .

$x^{2} + 3 x - 5 x - 15 = 0$

Subtract $5 x$ from $3 x$ .

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

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 $c = - 15$ into the quadratic formula and solve for $x$ .

$\frac{2 \pm \sqrt{{(- 2)}^{2} - 4 \cdot (1 \cdot - 15)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 1 \cdot - 15}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 15$ .

Multiply $- 4$ by $1$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot - 15}}{2 \cdot 1}$

Multiply $- 4$ by $- 15$ .

$x = \frac{2 \pm \sqrt{4 + 60}}{2 \cdot 1}$

Add $4$ and $60$ .

$x = \frac{2 \pm \sqrt{64}}{2 \cdot 1}$

Rewrite $64$ as $8^{2}$ .

$x = \frac{2 \pm \sqrt{8^{2}}}{2 \cdot 1}$

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

$x = \frac{2 \pm 8}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{2 \pm 8}{2}$

Simplify $\frac{2 \pm 8}{2}$ .

$x = 1 \pm 4$

Step 5

The final answer is the combination of both solutions.

$x = 5, - 3$

Solve Using the Quadratic Formula (x-5)(x+3)=0

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