Solve Using the Square Root Property (8x+20)^2=50

${(8 x + 20)}^{2} = 50$

Step 1

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

$8 x + 20 = \pm \sqrt{50}$

Step 2

Simplify $\pm \sqrt{50}$ .

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$8 x + 20 = \pm \sqrt{25 (2)}$

Rewrite $25$ as $5^{2}$ .

$8 x + 20 = \pm \sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$8 x + 20 = \pm 5 \sqrt{2}$

Step 3

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.

$8 x + 20 = 5 \sqrt{2}$

Subtract $20$ from both sides of the equation.

$8 x = 5 \sqrt{2} - 20$

Divide each term in $8 x = 5 \sqrt{2} - 20$ by $8$ and simplify.

Divide each term in $8 x = 5 \sqrt{2} - 20$ by $8$ .

$\frac{8 x}{8} = \frac{5 \sqrt{2}}{8} + \frac{- 20}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{5 \sqrt{2}}{8} + \frac{- 20}{8}$

Divide $x$ by $1$ .

$x = \frac{5 \sqrt{2}}{8} + \frac{- 20}{8}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 20$ and $8$ .

Factor $4$ out of $- 20$ .

$x = \frac{5 \sqrt{2}}{8} + \frac{4 (- 5)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$x = \frac{5 \sqrt{2}}{8} + \frac{4 \cdot - 5}{4 \cdot 2}$

Cancel the common factor.

$x = \frac{5 \sqrt{2}}{8} + \frac{4 \cdot - 5}{4 \cdot 2}$

Rewrite the expression.

$x = \frac{5 \sqrt{2}}{8} + \frac{- 5}{2}$

Move the negative in front of the fraction.

$x = \frac{5 \sqrt{2}}{8} - \frac{5}{2}$

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

$8 x + 20 = - 5 \sqrt{2}$

Subtract $20$ from both sides of the equation.

$8 x = - 5 \sqrt{2} - 20$

Divide each term in $8 x = - 5 \sqrt{2} - 20$ by $8$ and simplify.

Divide each term in $8 x = - 5 \sqrt{2} - 20$ by $8$ .

$\frac{8 x}{8} = \frac{- 5 \sqrt{2}}{8} + \frac{- 20}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 5 \sqrt{2}}{8} + \frac{- 20}{8}$

Divide $x$ by $1$ .

$x = \frac{- 5 \sqrt{2}}{8} + \frac{- 20}{8}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{5 \sqrt{2}}{8} + \frac{- 20}{8}$

Cancel the common factor of $- 20$ and $8$ .

Factor $4$ out of $- 20$ .

$x = - \frac{5 \sqrt{2}}{8} + \frac{4 (- 5)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$x = - \frac{5 \sqrt{2}}{8} + \frac{4 \cdot - 5}{4 \cdot 2}$

Cancel the common factor.

$x = - \frac{5 \sqrt{2}}{8} + \frac{4 \cdot - 5}{4 \cdot 2}$

Rewrite the expression.

$x = - \frac{5 \sqrt{2}}{8} + \frac{- 5}{2}$

Move the negative in front of the fraction.

$x = - \frac{5 \sqrt{2}}{8} - \frac{5}{2}$

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

$x = \frac{5 \sqrt{2}}{8} - \frac{5}{2}, - \frac{5 \sqrt{2}}{8} - \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5 \sqrt{2}}{8} - \frac{5}{2}, - \frac{5 \sqrt{2}}{8} - \frac{5}{2}$

Decimal Form:

$x = - 1.61611652 \dots, - 3.38388347 \dots$

Solve Using the Square Root Property (8x+20)^2=50

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