Algebra Examples

$4 x^{2} + n x = - 9$

Step 1

Subtract $4 x^{2}$ from both sides of the equation.

$n x = - 9 - 4 x^{2}$

Step 2

Divide each term in $n x = - 9 - 4 x^{2}$ by $x$ and simplify.

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Step 2.1

Divide each term in $n x = - 9 - 4 x^{2}$ by $x$ .

$\frac{n x}{x} = \frac{- 9}{x} + \frac{- 4 x^{2}}{x}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $x$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{n x}{x} = \frac{- 9}{x} + \frac{- 4 x^{2}}{x}$

Step 2.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 9}{x} + \frac{- 4 x^{2}}{x}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Move the negative in front of the fraction.

$n = - \frac{9}{x} + \frac{- 4 x^{2}}{x}$

Step 2.3.1.2

Cancel the common factor of $x^{2}$ and $x$ .

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Step 2.3.1.2.1

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

$n = - \frac{9}{x} + \frac{x (- 4 x)}{x}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Raise $x$ to the power of $1$ .

$n = - \frac{9}{x} + \frac{x (- 4 x)}{x^{1}}$

Step 2.3.1.2.2.2

Factor $x$ out of $x^{1}$ .

$n = - \frac{9}{x} + \frac{x (- 4 x)}{x \cdot 1}$

Step 2.3.1.2.2.3

Cancel the common factor.

$n = - \frac{9}{x} + \frac{x (- 4 x)}{x \cdot 1}$

Step 2.3.1.2.2.4

Rewrite the expression.

$n = - \frac{9}{x} + \frac{- 4 x}{1}$

Step 2.3.1.2.2.5

Divide $- 4 x$ by $1$ .

$n = - \frac{9}{x} - 4 x$