Solve for k (5k+2)^2=64

${(5 k + 2)}^{2} = 64$

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

$5 k + 2 = \pm \sqrt{64}$

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$5 k + 2 = \pm \sqrt{8^{2}}$

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

$5 k + 2 = \pm 8$

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.

$5 k + 2 = 8$

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

Subtract $2$ from both sides of the equation.

$5 k = 8 - 2$

Subtract $2$ from $8$ .

$5 k = 6$

Divide each term in $5 k = 6$ by $5$ and simplify.

Divide each term in $5 k = 6$ by $5$ .

$\frac{5 k}{5} = \frac{6}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 k}{5} = \frac{6}{5}$

Divide $k$ by $1$ .

$k = \frac{6}{5}$

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

$5 k + 2 = - 8$

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

Subtract $2$ from both sides of the equation.

$5 k = - 8 - 2$

Subtract $2$ from $- 8$ .

$5 k = - 10$

Divide each term in $5 k = - 10$ by $5$ and simplify.

Divide each term in $5 k = - 10$ by $5$ .

$\frac{5 k}{5} = \frac{- 10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 k}{5} = \frac{- 10}{5}$

Divide $k$ by $1$ .

$k = \frac{- 10}{5}$

Simplify the right side.

Divide $- 10$ by $5$ .

$k = - 2$

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

$k = \frac{6}{5}, - 2$

The result can be shown in multiple forms.

Exact Form:

$k = \frac{6}{5}, - 2$

Decimal Form:

$k = 1.2, - 2$

Mixed Number Form:

$k = 1 \frac{1}{5}, - 2$

Solve for k (5k+2)^2=64

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