Solve Using the Quadratic Formula (x-5)(x+8)=0

$(x - 5) (x + 8) = 0$

Simplify $(x - 5) (x + 8)$ .

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Expand $(x - 5) (x + 8)$ using the FOIL Method.

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Apply the distributive property.

$x (x + 8) - 5 (x + 8) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 8 - 5 (x + 8) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 8 - 5 x - 5 \cdot 8 = 0$

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

$x^{2} + x \cdot 8 - 5 x - 5 \cdot 8 = 0$

Move $8$ to the left of $x$ .

$x^{2} + 8 \cdot x - 5 x - 5 \cdot 8 = 0$

Multiply $- 5$ by $8$ .

$x^{2} + 8 x - 5 x - 40 = 0$

Subtract $5 x$ from $8 x$ .

$x^{2} + 3 x - 40 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = 3$ , and $c = - 40$ into the quadratic formula and solve for $x$ .

$\frac{- 3 \pm \sqrt{3^{2} - 4 \cdot (1 \cdot - 40)}}{2 \cdot 1}$

Simplify.

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Simplify the numerator.

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Raise $3$ to the power of $2$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot 1 \cdot - 40}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot - 40}}{2 \cdot 1}$

Multiply $- 4$ by $- 40$ .

$x = \frac{- 3 \pm \sqrt{9 + 160}}{2 \cdot 1}$

Add $9$ and $160$ .

$x = \frac{- 3 \pm \sqrt{169}}{2 \cdot 1}$

Rewrite $169$ as $13^{2}$ .

$x = \frac{- 3 \pm \sqrt{13^{2}}}{2 \cdot 1}$

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

$x = \frac{- 3 \pm 13}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 3 \pm 13}{2}$

The final answer is the combination of both solutions.

$x = 5, - 8$

Solve Using the Quadratic Formula (x-5)(x+8)=0

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