Solve Using the Quadratic Formula (x-12)(x+4)=9

$(x - 12) (x + 4) = 9$

Step 1

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

Simplify the left side.

Simplify $(x - 12) (x + 4)$ .

Expand $(x - 12) (x + 4)$ using the FOIL Method.

Apply the distributive property.

$x (x + 4) - 12 (x + 4) = 9$

Apply the distributive property.

$x \cdot x + x \cdot 4 - 12 (x + 4) = 9$

Apply the distributive property.

$x \cdot x + x \cdot 4 - 12 x - 12 \cdot 4 = 9$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 4 - 12 x - 12 \cdot 4 = 9$

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

$x^{2} + 4 \cdot x - 12 x - 12 \cdot 4 = 9$

Multiply $- 12$ by $4$ .

$x^{2} + 4 x - 12 x - 48 = 9$

Subtract $12 x$ from $4 x$ .

$x^{2} - 8 x - 48 = 9$

Subtract $9$ from both sides of the equation.

$x^{2} - 8 x - 48 - 9 = 0$

Subtract $9$ from $- 48$ .

$x^{2} - 8 x - 57 = 0$

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 $a = 1$ , $b = - 8$ , and $c = - 57$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot - 57)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 57}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 57$ .

Multiply $- 4$ by $1$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot - 57}}{2 \cdot 1}$

Multiply $- 4$ by $- 57$ .

$x = \frac{8 \pm \sqrt{64 + 228}}{2 \cdot 1}$

Add $64$ and $228$ .

$x = \frac{8 \pm \sqrt{292}}{2 \cdot 1}$

Rewrite $292$ as $2^{2} \cdot 73$ .

Factor $4$ out of $292$ .

$x = \frac{8 \pm \sqrt{4 (73)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{8 \pm \sqrt{2^{2} \cdot 73}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{8 \pm 2 \sqrt{73}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{8 \pm 2 \sqrt{73}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{73}}{2}$ .

$x = 4 \pm \sqrt{73}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 4 \pm \sqrt{73}$

Decimal Form:

$x = 12.54400374 \dots, - 4.54400374 \dots$

Solve Using the Quadratic Formula (x-12)(x+4)=9

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