Pre-Algebra Examples

$\frac{1}{16} x^{2} + \frac{1}{8} x = \frac{1}{2}$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{16}$ and $x^{2}$ .

$\frac{x^{2}}{16} + \frac{1}{8} x = \frac{1}{2}$

Step 1.2

Combine $\frac{1}{8}$ and $x$ .

$\frac{x^{2}}{16} + \frac{x}{8} = \frac{1}{2}$

Step 2

Multiply each term in $\frac{x^{2}}{16} + \frac{x}{8} = \frac{1}{2}$ by $16$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{x^{2}}{16} + \frac{x}{8} = \frac{1}{2}$ by $16$ .

$\frac{x^{2}}{16} \cdot 16 + \frac{x}{8} \cdot 16 = \frac{1}{2} \cdot 16$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Cancel the common factor of $16$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{x^{2}}{16} \cdot 16 + \frac{x}{8} \cdot 16 = \frac{1}{2} \cdot 16$

Step 2.2.1.1.2

Rewrite the expression.

$x^{2} + \frac{x}{8} \cdot 16 = \frac{1}{2} \cdot 16$

Step 2.2.1.2

Cancel the common factor of $8$ .

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Step 2.2.1.2.1

Factor $8$ out of $16$ .

$x^{2} + \frac{x}{8} \cdot (8 (2)) = \frac{1}{2} \cdot 16$

Step 2.2.1.2.2

Cancel the common factor.

$x^{2} + \frac{x}{8} \cdot (8 \cdot 2) = \frac{1}{2} \cdot 16$

Step 2.2.1.2.3

Rewrite the expression.

$x^{2} + x \cdot 2 = \frac{1}{2} \cdot 16$

Step 2.2.1.3

Move $2$ to the left of $x$ .

$x^{2} + 2 x = \frac{1}{2} \cdot 16$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $2$ .

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Step 2.3.1.1

Factor $2$ out of $16$ .

$x^{2} + 2 x = \frac{1}{2} \cdot (2 (8))$

Step 2.3.1.2

Cancel the common factor.

$x^{2} + 2 x = \frac{1}{2} \cdot (2 \cdot 8)$

Step 2.3.1.3

Rewrite the expression.

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

Step 3

Subtract $8$ from both sides of the equation.

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

Step 4

Factor $x^{2} + 2 x - 8$ using the AC method.

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Step 4.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 8$ and whose sum is $2$ .

$- 2, 4$

Step 4.2

Write the factored form using these integers.

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

Step 5

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 2 = 0$

$x + 4 = 0$

Step 6

Set $x - 2$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Step 6.2

Add $2$ to both sides of the equation.

$x = 2$

Step 7

Set $x + 4$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Step 7.2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 8

The final solution is all the values that make $(x - 2) (x + 4) = 0$ true.

$x = 2, - 4$