Solve Using the Quadratic Formula (x-4)(x+6)=11

$(x - 4) (x + 6) = 11$

Step 1

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

Simplify the left side.

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

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

Apply the distributive property.

$x (x + 6) - 4 (x + 6) = 11$

Apply the distributive property.

$x \cdot x + x \cdot 6 - 4 (x + 6) = 11$

Apply the distributive property.

$x \cdot x + x \cdot 6 - 4 x - 4 \cdot 6 = 11$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 6 - 4 x - 4 \cdot 6 = 11$

Move $6$ to the left of $x$ .

$x^{2} + 6 \cdot x - 4 x - 4 \cdot 6 = 11$

Multiply $- 4$ by $6$ .

$x^{2} + 6 x - 4 x - 24 = 11$

Subtract $4 x$ from $6 x$ .

$x^{2} + 2 x - 24 = 11$

Subtract $11$ from both sides of the equation.

$x^{2} + 2 x - 24 - 11 = 0$

Subtract $11$ from $- 24$ .

$x^{2} + 2 x - 35 = 0$

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 $c = - 35$ into the quadratic formula and solve for $x$ .

$\frac{- 2 \pm \sqrt{2^{2} - 4 \cdot (1 \cdot - 35)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot 1 \cdot - 35}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 35$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot - 35}}{2 \cdot 1}$

Multiply $- 4$ by $- 35$ .

$x = \frac{- 2 \pm \sqrt{4 + 140}}{2 \cdot 1}$

Add $4$ and $140$ .

$x = \frac{- 2 \pm \sqrt{144}}{2 \cdot 1}$

Rewrite $144$ as $12^{2}$ .

$x = \frac{- 2 \pm \sqrt{12^{2}}}{2 \cdot 1}$

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

$x = \frac{- 2 \pm 12}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 2 \pm 12}{2}$

Simplify $\frac{- 2 \pm 12}{2}$ .

$x = - 1 \pm 6$

Step 5

The final answer is the combination of both solutions.

$x = 5, - 7$

Solve Using the Quadratic Formula (x-4)(x+6)=11

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