Solve Using the Quadratic Formula (x+6)(x-4)=-16

$(x + 6) (x - 4) = - 16$

Step 1

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

Simplify the left side.

Simplify $(x + 6) (x - 4)$ .

Expand $(x + 6) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$x (x - 4) + 6 (x - 4) = - 16$

Apply the distributive property.

$x \cdot x + x \cdot - 4 + 6 (x - 4) = - 16$

Apply the distributive property.

$x \cdot x + x \cdot - 4 + 6 x + 6 \cdot - 4 = - 16$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 4 + 6 x + 6 \cdot - 4 = - 16$

Move $- 4$ to the left of $x$ .

$x^{2} - 4 \cdot x + 6 x + 6 \cdot - 4 = - 16$

Multiply $6$ by $- 4$ .

$x^{2} - 4 x + 6 x - 24 = - 16$

Add $- 4 x$ and $6 x$ .

$x^{2} + 2 x - 24 = - 16$

Add $16$ to both sides of the equation.

$x^{2} + 2 x - 24 + 16 = 0$

Add $- 24$ and $16$ .

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

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 $c = - 8$ into the quadratic formula and solve for $x$ .

$\frac{- 2 \pm \sqrt{2^{2} - 4 \cdot (1 \cdot - 8)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot 1 \cdot - 8}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 8$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot - 8}}{2 \cdot 1}$

Multiply $- 4$ by $- 8$ .

$x = \frac{- 2 \pm \sqrt{4 + 32}}{2 \cdot 1}$

Add $4$ and $32$ .

$x = \frac{- 2 \pm \sqrt{36}}{2 \cdot 1}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{- 2 \pm \sqrt{6^{2}}}{2 \cdot 1}$

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

$x = \frac{- 2 \pm 6}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 2 \pm 6}{2}$

Simplify $\frac{- 2 \pm 6}{2}$ .

$x = - 1 \pm 3$

Step 5

The final answer is the combination of both solutions.

$x = 2, - 4$

Solve Using the Quadratic Formula (x+6)(x-4)=-16

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