Solve Using the Square Root Property (3k+4)^2=25

${(3 k + 4)}^{2} = 25$

Step 1

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

$3 k + 4 = \pm \sqrt{25}$

Step 2

Simplify $\pm \sqrt{25}$ .

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

$3 k + 4 = \pm \sqrt{5^{2}}$

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

$3 k + 4 = \pm 5$

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.

$3 k + 4 = 5$

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

Subtract $4$ from both sides of the equation.

$3 k = 5 - 4$

Subtract $4$ from $5$ .

$3 k = 1$

Divide each term in $3 k = 1$ by $3$ and simplify.

Divide each term in $3 k = 1$ by $3$ .

$\frac{3 k}{3} = \frac{1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 k}{3} = \frac{1}{3}$

Divide $k$ by $1$ .

$k = \frac{1}{3}$

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

$3 k + 4 = - 5$

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

Subtract $4$ from both sides of the equation.

$3 k = - 5 - 4$

Subtract $4$ from $- 5$ .

$3 k = - 9$

Divide each term in $3 k = - 9$ by $3$ and simplify.

Divide each term in $3 k = - 9$ by $3$ .

$\frac{3 k}{3} = \frac{- 9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 k}{3} = \frac{- 9}{3}$

Divide $k$ by $1$ .

$k = \frac{- 9}{3}$

Simplify the right side.

Divide $- 9$ by $3$ .

$k = - 3$

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

$k = \frac{1}{3}, - 3$

Solve Using the Square Root Property (3k+4)^2=25

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