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

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

Take the square root of each side of the equation to set up the solution for $x$

${(2 x + 5)}^{2 \cdot \frac{1}{2}} = \pm \sqrt{7}$

Remove the perfect root factor $2 x + 5$ under the radical to solve for $x$ .

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

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

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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 by $2$ and simplify.

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

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 by $2$ and simplify.

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

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

Cancel the common factor of $2$ .

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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 each term.

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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.

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

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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