Finite Math Examples

$(x + 2) (x + 4)$

Step 1

Set $(x + 2) (x + 4)$ equal to $0$ .

$(x + 2) (x + 4) = 0$

Step 2

Simplify the left side.

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Step 2.1

Simplify $(x + 2) (x + 4)$ .

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Step 2.1.1

Expand $(x + 2) (x + 4)$ using the FOIL Method.

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Step 2.1.1.1

Apply the distributive property.

$x (x + 4) + 2 (x + 4) = 0$

Step 2.1.1.2

Apply the distributive property.

$x \cdot x + x \cdot 4 + 2 (x + 4) = 0$

Step 2.1.1.3

Apply the distributive property.

$x \cdot x + x \cdot 4 + 2 x + 2 \cdot 4 = 0$

Step 2.1.2

Simplify and combine like terms.

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Step 2.1.2.1

Simplify each term.

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Step 2.1.2.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 4 + 2 x + 2 \cdot 4 = 0$

Step 2.1.2.1.2

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

$x^{2} + 4 \cdot x + 2 x + 2 \cdot 4 = 0$

Step 2.1.2.1.3

Multiply $2$ by $4$ .

$x^{2} + 4 x + 2 x + 8 = 0$

Step 2.1.2.2

Add $4 x$ and $2 x$ .

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

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = 1$ , $b = 6$ , and $c = 8$ into the quadratic formula and solve for $x$ .

$\frac{- 6 \pm \sqrt{6^{2} - 4 \cdot (1 \cdot 8)}}{2 \cdot 1}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $6$ to the power of $2$ .

$x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 1 \cdot 8}}{2 \cdot 1}$

Step 5.1.2

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

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Step 5.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 8}}{2 \cdot 1}$

Step 5.1.2.2

Multiply $- 4$ by $8$ .

$x = \frac{- 6 \pm \sqrt{36 - 32}}{2 \cdot 1}$

Step 5.1.3

Subtract $32$ from $36$ .

$x = \frac{- 6 \pm \sqrt{4}}{2 \cdot 1}$

Step 5.1.4

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

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

Step 5.1.5

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

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

Step 5.2

Multiply $2$ by $1$ .

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

Step 5.3

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

$x = - 3 \pm 1$

Step 6

The final answer is the combination of both solutions.

$x = - 2, - 4$