Solve for x 5x(x+6)=-50

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

Step 1

Divide each term in $5 x (x + 6) = - 50$ by $5$ and simplify.

Divide each term in $5 x (x + 6) = - 50$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x (x + 6)$ by $1$ .

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

Apply the distributive property.

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

Simplify the expression.

Multiply $x$ by $x$ .

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

Move $6$ to the left of $x$ .

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

Simplify the right side.

Divide $- 50$ by $5$ .

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

Step 2

Add $10$ to both sides of the equation.

$x^{2} + 6 x + 10 = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = 1$ , $b = 6$ , and $c = 10$ into the quadratic formula and solve for $x$ .

$\frac{- 6 \pm \sqrt{6^{2} - 4 \cdot (1 \cdot 10)}}{2 \cdot 1}$

Step 5

Simplify.

Simplify the numerator.

Raise $6$ to the power of $2$ .

$x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 1 \cdot 10}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 10$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 10}}{2 \cdot 1}$

Multiply $- 4$ by $10$ .

$x = \frac{- 6 \pm \sqrt{36 - 40}}{2 \cdot 1}$

Subtract $40$ from $36$ .

$x = \frac{- 6 \pm \sqrt{- 4}}{2 \cdot 1}$

Rewrite $- 4$ as $- 1 (4)$ .

$x = \frac{- 6 \pm \sqrt{- 1 \cdot 4}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$x = \frac{- 6 \pm \sqrt{- 1} \cdot \sqrt{4}}{2 \cdot 1}$

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

$x = \frac{- 6 \pm i \cdot \sqrt{4}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 6 \pm i \cdot \sqrt{2^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 6 \pm i \cdot 2}{2 \cdot 1}$

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

$x = \frac{- 6 \pm 2 i}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 6 \pm 2 i}{2}$

Simplify $\frac{- 6 \pm 2 i}{2}$ .

$x = - 3 \pm i$

Step 6

The final answer is the combination of both solutions.

$x = - 3 + i, - 3 - i$

Solve for x 5x(x+6)=-50

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