Solve Using the Quadratic Formula 5(x+11)^2=-50

$5 {(x + 11)}^{2} = - 50$

Move all terms to the left side of the equation and simplify.

Add $50$ to both sides of the equation.

$5 {(x + 11)}^{2} + 50 = 0$

Simplify $5 {(x + 11)}^{2} + 50$ .

Simplify each term.

Rewrite ${(x + 11)}^{2}$ as $(x + 11) (x + 11)$ .

$5 ((x + 11) (x + 11)) + 50 = 0$

Expand $(x + 11) (x + 11)$ using the FOIL Method.

Apply the distributive property.

$5 (x (x + 11) + 11 (x + 11)) + 50 = 0$

Apply the distributive property.

$5 (x \cdot x + x \cdot 11 + 11 (x + 11)) + 50 = 0$

Apply the distributive property.

$5 (x \cdot x + x \cdot 11 + 11 x + 11 \cdot 11) + 50 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$5 (x^{2} + x \cdot 11 + 11 x + 11 \cdot 11) + 50 = 0$

Move $11$ to the left of $x$ .

$5 (x^{2} + 11 \cdot x + 11 x + 11 \cdot 11) + 50 = 0$

Multiply $11$ by $11$ .

$5 (x^{2} + 11 x + 11 x + 121) + 50 = 0$

Add $11 x$ and $11 x$ .

$5 (x^{2} + 22 x + 121) + 50 = 0$

Apply the distributive property.

$5 x^{2} + 5 (22 x) + 5 \cdot 121 + 50 = 0$

Simplify.

Multiply $22$ by $5$ .

$5 x^{2} + 110 x + 5 \cdot 121 + 50 = 0$

Multiply $5$ by $121$ .

$5 x^{2} + 110 x + 605 + 50 = 0$

Add $605$ and $50$ .

$5 x^{2} + 110 x + 655 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 5$ , $b = 110$ , and $c = 655$ into the quadratic formula and solve for $x$ .

$\frac{- 110 \pm \sqrt{110^{2} - 4 \cdot (5 \cdot 655)}}{2 \cdot 5}$

Simplify.

Simplify the numerator.

Raise $110$ to the power of $2$ .

$x = \frac{- 110 \pm \sqrt{12100 - 4 \cdot 5 \cdot 655}}{2 \cdot 5}$

Multiply $- 4$ by $5$ .

$x = \frac{- 110 \pm \sqrt{12100 - 20 \cdot 655}}{2 \cdot 5}$

Multiply $- 20$ by $655$ .

$x = \frac{- 110 \pm \sqrt{12100 - 13100}}{2 \cdot 5}$

Subtract $13100$ from $12100$ .

$x = \frac{- 110 \pm \sqrt{- 1000}}{2 \cdot 5}$

Rewrite $- 1000$ as $- 1 (1000)$ .

$x = \frac{- 110 \pm \sqrt{- 1 \cdot 1000}}{2 \cdot 5}$

Rewrite $\sqrt{- 1 (1000)}$ as $\sqrt{- 1} \cdot \sqrt{1000}$ .

$x = \frac{- 110 \pm \sqrt{- 1} \cdot \sqrt{1000}}{2 \cdot 5}$

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

$x = \frac{- 110 \pm i \cdot \sqrt{1000}}{2 \cdot 5}$

Rewrite $1000$ as $10^{2} \cdot 10$ .

Factor $100$ out of $1000$ .

$x = \frac{- 110 \pm i \cdot \sqrt{100 (10)}}{2 \cdot 5}$

Rewrite $100$ as $10^{2}$ .

$x = \frac{- 110 \pm i \cdot \sqrt{10^{2} \cdot 10}}{2 \cdot 5}$

Pull terms out from under the radical.

$x = \frac{- 110 \pm i \cdot (10 \sqrt{10})}{2 \cdot 5}$

Move $10$ to the left of $i$ .

$x = \frac{- 110 \pm 10 i \sqrt{10}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{- 110 \pm 10 i \sqrt{10}}{10}$

Simplify $\frac{- 110 \pm 10 i \sqrt{10}}{10}$ .

$x = - 11 \pm i \sqrt{10}$

Solve Using the Quadratic Formula 5(x+11)^2=-50

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