Algebra Examples

$5 x (x + 6) = - 50$

Step 1

Simplify $5 x (x + 6)$ .

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Step 1.1

Apply the distributive property.

$5 x \cdot x + 5 x \cdot 6 = - 50$

Step 1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 1.2.1

Move $x$ .

$5 (x \cdot x) + 5 x \cdot 6 = - 50$

Step 1.2.2

Multiply $x$ by $x$ .

$5 x^{2} + 5 x \cdot 6 = - 50$

Step 1.3

Multiply $6$ by $5$ .

$5 x^{2} + 30 x = - 50$

Step 2

Divide each term in $5 x^{2} + 30 x = - 50$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 x^{2} + 30 x = - 50$ by $5$ .

$\frac{5 x^{2}}{5} + \frac{30 x}{5} = \frac{- 50}{5}$

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.

$\frac{5 x^{2}}{5} + \frac{30 x}{5} = \frac{- 50}{5}$

Step 2.2.1.1.2

Divide $x^{2}$ by $1$ .

$x^{2} + \frac{30 x}{5} = \frac{- 50}{5}$

Step 2.2.1.2

Cancel the common factor of $30$ and $5$ .

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Step 2.2.1.2.1

Factor $5$ out of $30 x$ .

$x^{2} + \frac{5 (6 x)}{5} = \frac{- 50}{5}$

Step 2.2.1.2.2

Cancel the common factors.

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Step 2.2.1.2.2.1

Factor $5$ out of $5$ .

$x^{2} + \frac{5 (6 x)}{5 (1)} = \frac{- 50}{5}$

Step 2.2.1.2.2.2

Cancel the common factor.

$x^{2} + \frac{5 (6 x)}{5 \cdot 1} = \frac{- 50}{5}$

Step 2.2.1.2.2.3

Rewrite the expression.

$x^{2} + \frac{6 x}{1} = \frac{- 50}{5}$

Step 2.2.1.2.2.4

Divide $6 x$ by $1$ .

$x^{2} + 6 x = \frac{- 50}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 50$ by $5$ .

$x^{2} + 6 x = - 10$

Step 3

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(3)}^{2}$

Step 4

Add the term to each side of the equation.

$x^{2} + 6 x + {(3)}^{2} = - 10 + {(3)}^{2}$

Step 5

Simplify the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Raise $3$ to the power of $2$ .

$x^{2} + 6 x + 9 = - 10 + {(3)}^{2}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- 10 + {(3)}^{2}$ .

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Step 5.2.1.1

Raise $3$ to the power of $2$ .

$x^{2} + 6 x + 9 = - 10 + 9$

Step 5.2.1.2

Add $- 10$ and $9$ .

$x^{2} + 6 x + 9 = - 1$

Step 6

Factor the perfect trinomial square into ${(x + 3)}^{2}$ .

${(x + 3)}^{2} = - 1$

Step 7

Solve the equation for $x$ .

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Step 7.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x + 3 = \pm \sqrt{- 1}$

Step 7.2

Rewrite $\sqrt{- 1}$ as $i$ .

$x + 3 = \pm i$

Step 7.3

Move all terms not containing $x$ to the right side of the equation.

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Step 7.3.1

Subtract $3$ from both sides of the equation.

$x = \pm i - 3$

Step 7.3.2

Reorder $\pm i$ and $- 3$ .

$x = - 3 \pm i$