Solve Using the Quadratic Formula (x-6)(x+8)=0

$(x - 6) (x + 8) = 0$

Step 1

Simplify the left side.

Simplify $(x - 6) (x + 8)$ .

Expand $(x - 6) (x + 8)$ using the FOIL Method.

Apply the distributive property.

$x (x + 8) - 6 (x + 8) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 8 - 6 (x + 8) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 8 - 6 x - 6 \cdot 8 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 8 - 6 x - 6 \cdot 8 = 0$

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

$x^{2} + 8 \cdot x - 6 x - 6 \cdot 8 = 0$

Multiply $- 6$ by $8$ .

$x^{2} + 8 x - 6 x - 48 = 0$

Subtract $6 x$ from $8 x$ .

$x^{2} + 2 x - 48 = 0$

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 $c = - 48$ into the quadratic formula and solve for $x$ .

$\frac{- 2 \pm \sqrt{2^{2} - 4 \cdot (1 \cdot - 48)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot 1 \cdot - 48}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 48$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot - 48}}{2 \cdot 1}$

Multiply $- 4$ by $- 48$ .

$x = \frac{- 2 \pm \sqrt{4 + 192}}{2 \cdot 1}$

Add $4$ and $192$ .

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

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

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

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

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

Multiply $2$ by $1$ .

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

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

$x = - 1 \pm 7$

Step 5

The final answer is the combination of both solutions.

$x = 6, - 8$

Solve Using the Quadratic Formula (x-6)(x+8)=0

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