Precalculus Examples

$8 x^{2} + 14 x = 0$

Step 1

Factor $2 x$ out of $8 x^{2} + 14 x$ .

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Step 1.1

Factor $2 x$ out of $8 x^{2}$ .

$2 x (4 x) + 14 x = 0$

Step 1.2

Factor $2 x$ out of $14 x$ .

$2 x (4 x) + 2 x (7) = 0$

Step 1.3

Factor $2 x$ out of $2 x (4 x) + 2 x (7)$ .

$2 x (4 x + 7) = 0$

Step 2

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

$x = 0$

$4 x + 7 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $4 x + 7$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $4 x + 7$ equal to $0$ .

$4 x + 7 = 0$

Step 4.2

Solve $4 x + 7 = 0$ for $x$ .

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Step 4.2.1

Subtract $7$ from both sides of the equation.

$4 x = - 7$

Step 4.2.2

Divide each term in $4 x = - 7$ by $4$ and simplify.

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Step 4.2.2.1

Divide each term in $4 x = - 7$ by $4$ .

$\frac{4 x}{4} = \frac{- 7}{4}$

Step 4.2.2.2

Simplify the left side.

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Step 4.2.2.2.1

Cancel the common factor of $4$ .

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Step 4.2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 7}{4}$

Step 4.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{4}$

Step 4.2.2.3

Simplify the right side.

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Step 4.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{7}{4}$

Step 5

The final solution is all the values that make $2 x (4 x + 7) = 0$ true.

$x = 0, - \frac{7}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 0, - \frac{7}{4}$

Decimal Form:

$x = 0, - 1.75$

Mixed Number Form:

$x = 0, - 1 \frac{3}{4}$