Solve Using the Square Root Property (2x+5)^2=7

${(2 x + 5)}^{2} = 7$

Step 1

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

$2 x + 5 = \pm \sqrt{7}$

Step 2

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.

$2 x + 5 = \sqrt{7}$

Subtract $5$ from both sides of the equation.

$2 x = \sqrt{7} - 5$

Divide each term in $2 x = \sqrt{7} - 5$ by $2$ and simplify.

Divide each term in $2 x = \sqrt{7} - 5$ by $2$ .

$\frac{2 x}{2} = \frac{\sqrt{7}}{2} + \frac{- 5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{\sqrt{7}}{2} + \frac{- 5}{2}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{7}}{2} + \frac{- 5}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{\sqrt{7}}{2} - \frac{5}{2}$

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

$2 x + 5 = - \sqrt{7}$

Subtract $5$ from both sides of the equation.

$2 x = - \sqrt{7} - 5$

Divide each term in $2 x = - \sqrt{7} - 5$ by $2$ and simplify.

Divide each term in $2 x = - \sqrt{7} - 5$ by $2$ .

$\frac{2 x}{2} = \frac{- \sqrt{7}}{2} + \frac{- 5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- \sqrt{7}}{2} + \frac{- 5}{2}$

Divide $x$ by $1$ .

$x = \frac{- \sqrt{7}}{2} + \frac{- 5}{2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{\sqrt{7}}{2} + \frac{- 5}{2}$

Move the negative in front of the fraction.

$x = - \frac{\sqrt{7}}{2} - \frac{5}{2}$

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

$x = \frac{\sqrt{7}}{2} - \frac{5}{2}, - \frac{\sqrt{7}}{2} - \frac{5}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{7}}{2} - \frac{5}{2}, - \frac{\sqrt{7}}{2} - \frac{5}{2}$

Decimal Form:

$x = - 1.17712434 \dots, - 3.82287565 \dots$

Solve Using the Square Root Property (2x+5)^2=7

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