Solve Using the Square Root Property (5x+2)^2+100=0

${(5 x + 2)}^{2} + 100 = 0$

Step 1

Subtract $100$ from both sides of the equation.

${(5 x + 2)}^{2} = - 100$

Step 2

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

$5 x + 2 = \pm \sqrt{- 100}$

Step 3

Simplify $\pm \sqrt{- 100}$ .

Rewrite $- 100$ as $- 1 (100)$ .

$5 x + 2 = \pm \sqrt{- 1 (100)}$

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$5 x + 2 = \pm \sqrt{- 1} \cdot \sqrt{100}$

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

$5 x + 2 = \pm i \cdot \sqrt{100}$

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

$5 x + 2 = \pm i \cdot \sqrt{10^{2}}$

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

$5 x + 2 = \pm i \cdot 10$

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

$5 x + 2 = \pm 10 i$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$5 x + 2 = 10 i$

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

Subtract $2$ from both sides of the equation.

$5 x = 10 i - 2$

Reorder $10 i$ and $- 2$ .

$5 x = - 2 + 10 i$

Divide each term in $5 x = - 2 + 10 i$ by $5$ and simplify.

Divide each term in $5 x = - 2 + 10 i$ by $5$ .

$\frac{5 x}{5} = \frac{- 2}{5} + \frac{10 i}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 2}{5} + \frac{10 i}{5}$

Divide $x$ by $1$ .

$x = \frac{- 2}{5} + \frac{10 i}{5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{2}{5} + \frac{10 i}{5}$

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 i$ .

$x = - \frac{2}{5} + \frac{5 (2 i)}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$x = - \frac{2}{5} + \frac{5 (2 i)}{5 (1)}$

Cancel the common factor.

$x = - \frac{2}{5} + \frac{5 (2 i)}{5 \cdot 1}$

Rewrite the expression.

$x = - \frac{2}{5} + \frac{2 i}{1}$

Divide $2 i$ by $1$ .

$x = - \frac{2}{5} + 2 i$

Next, use the negative value of the $\pm$ to find the second solution.

$5 x + 2 = - 10 i$

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

Subtract $2$ from both sides of the equation.

$5 x = - 10 i - 2$

Reorder $- 10 i$ and $- 2$ .

$5 x = - 2 - 10 i$

Divide each term in $5 x = - 2 - 10 i$ by $5$ and simplify.

Divide each term in $5 x = - 2 - 10 i$ by $5$ .

$\frac{5 x}{5} = \frac{- 2}{5} + \frac{- 10 i}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 2}{5} + \frac{- 10 i}{5}$

Divide $x$ by $1$ .

$x = \frac{- 2}{5} + \frac{- 10 i}{5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{2}{5} + \frac{- 10 i}{5}$

Cancel the common factor of $- 10$ and $5$ .

Factor $5$ out of $- 10 i$ .

$x = - \frac{2}{5} + \frac{5 (- 2 i)}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$x = - \frac{2}{5} + \frac{5 (- 2 i)}{5 (1)}$

Cancel the common factor.

$x = - \frac{2}{5} + \frac{5 (- 2 i)}{5 \cdot 1}$

Rewrite the expression.

$x = - \frac{2}{5} + \frac{- 2 i}{1}$

Divide $- 2 i$ by $1$ .

$x = - \frac{2}{5} - 2 i$

The complete solution is the result of both the positive and negative portions of the solution.

$x = - \frac{2}{5} + 2 i, - \frac{2}{5} - 2 i$

Solve Using the Square Root Property (5x+2)^2+100=0

Related Questions

Support LCMGCF.com by disabling your adblocker.