Solve Using the Square Root Property (7x+4)^2=81

${(7 x + 4)}^{2} = 81$

Step 1

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

$7 x + 4 = \pm \sqrt{81}$

Step 2

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$7 x + 4 = \pm \sqrt{9^{2}}$

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

$7 x + 4 = \pm 9$

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.

$7 x + 4 = 9$

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

Subtract $4$ from both sides of the equation.

$7 x = 9 - 4$

Subtract $4$ from $9$ .

$7 x = 5$

Divide each term in $7 x = 5$ by $7$ and simplify.

Divide each term in $7 x = 5$ by $7$ .

$\frac{7 x}{7} = \frac{5}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{5}{7}$

Divide $x$ by $1$ .

$x = \frac{5}{7}$

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

$7 x + 4 = - 9$

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

Subtract $4$ from both sides of the equation.

$7 x = - 9 - 4$

Subtract $4$ from $- 9$ .

$7 x = - 13$

Divide each term in $7 x = - 13$ by $7$ and simplify.

Divide each term in $7 x = - 13$ by $7$ .

$\frac{7 x}{7} = \frac{- 13}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 13}{7}$

Divide $x$ by $1$ .

$x = \frac{- 13}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{13}{7}$

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

$x = \frac{5}{7}, - \frac{13}{7}$

Solve Using the Square Root Property (7x+4)^2=81

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