Pre-Algebra Examples

$\frac{2}{5} x^{2} + \frac{4}{5} x - \frac{16}{5} = 0$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{2}{5}$ and $x^{2}$ .

$\frac{2 x^{2}}{5} + \frac{4}{5} x - \frac{16}{5} = 0$

Step 1.2

Combine $\frac{4}{5}$ and $x$ .

$\frac{2 x^{2}}{5} + \frac{4 x}{5} - \frac{16}{5} = 0$

Step 2

Multiply each term in $\frac{2 x^{2}}{5} + \frac{4 x}{5} - \frac{16}{5} = 0$ by $5$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{2 x^{2}}{5} + \frac{4 x}{5} - \frac{16}{5} = 0$ by $5$ .

$\frac{2 x^{2}}{5} \cdot 5 + \frac{4 x}{5} \cdot 5 - \frac{16}{5} \cdot 5 = 0 \cdot 5$

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 $5$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{2 x^{2}}{5} \cdot 5 + \frac{4 x}{5} \cdot 5 - \frac{16}{5} \cdot 5 = 0 \cdot 5$

Step 2.2.1.1.2

Rewrite the expression.

$2 x^{2} + \frac{4 x}{5} \cdot 5 - \frac{16}{5} \cdot 5 = 0 \cdot 5$

Step 2.2.1.2

Cancel the common factor of $5$ .

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Step 2.2.1.2.1

Cancel the common factor.

$2 x^{2} + \frac{4 x}{5} \cdot 5 - \frac{16}{5} \cdot 5 = 0 \cdot 5$

Step 2.2.1.2.2

Rewrite the expression.

$2 x^{2} + 4 x - \frac{16}{5} \cdot 5 = 0 \cdot 5$

Step 2.2.1.3

Cancel the common factor of $5$ .

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Step 2.2.1.3.1

Move the leading negative in $- \frac{16}{5}$ into the numerator.

$2 x^{2} + 4 x + \frac{- 16}{5} \cdot 5 = 0 \cdot 5$

Step 2.2.1.3.2

Cancel the common factor.

$2 x^{2} + 4 x + \frac{- 16}{5} \cdot 5 = 0 \cdot 5$

Step 2.2.1.3.3

Rewrite the expression.

$2 x^{2} + 4 x - 16 = 0 \cdot 5$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $0$ by $5$ .

$2 x^{2} + 4 x - 16 = 0$

Step 3

Factor the left side of the equation.

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Step 3.1

Factor $2$ out of $2 x^{2} + 4 x - 16$ .

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Step 3.1.1

Factor $2$ out of $2 x^{2}$ .

$2 (x^{2}) + 4 x - 16 = 0$

Step 3.1.2

Factor $2$ out of $4 x$ .

$2 (x^{2}) + 2 (2 x) - 16 = 0$

Step 3.1.3

Factor $2$ out of $- 16$ .

$2 x^{2} + 2 (2 x) + 2 \cdot - 8 = 0$

Step 3.1.4

Factor $2$ out of $2 x^{2} + 2 (2 x)$ .

$2 (x^{2} + 2 x) + 2 \cdot - 8 = 0$

Step 3.1.5

Factor $2$ out of $2 (x^{2} + 2 x) + 2 \cdot - 8$ .

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

Step 3.2

Factor.

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Step 3.2.1

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

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Step 3.2.1.1

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 3.2.1.2

Write the factored form using these integers.

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

Step 3.2.2

Remove unnecessary parentheses.

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

Step 4

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 5

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

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Step 5.1

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

$x - 2 = 0$

Step 5.2

Add $2$ to both sides of the equation.

$x = 2$

Step 6

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

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Step 6.1

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

$x + 4 = 0$

Step 6.2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 7

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

$x = 2, - 4$