Solve for k (3k+2)^2=49

${(3 k + 2)}^{2} = 49$

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

$3 k + 2 = \pm \sqrt{49}$

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$3 k + 2 = \pm \sqrt{7^{2}}$

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

$3 k + 2 = \pm 7$

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.

$3 k + 2 = 7$

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

Subtract $2$ from both sides of the equation.

$3 k = 7 - 2$

Subtract $2$ from $7$ .

$3 k = 5$

Divide each term in $3 k = 5$ by $3$ and simplify.

Divide each term in $3 k = 5$ by $3$ .

$\frac{3 k}{3} = \frac{5}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 k}{3} = \frac{5}{3}$

Divide $k$ by $1$ .

$k = \frac{5}{3}$

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

$3 k + 2 = - 7$

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

Subtract $2$ from both sides of the equation.

$3 k = - 7 - 2$

Subtract $2$ from $- 7$ .

$3 k = - 9$

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.

$k = \frac{5}{3}, - 3$

The result can be shown in multiple forms.

Exact Form:

$k = \frac{5}{3}, - 3$

Decimal Form:

$k = 1.\overline{6}, - 3$

Mixed Number Form:

$k = 1 \frac{2}{3}, - 3$

Solve for k (3k+2)^2=49

Related Questions

Support LCMGCF.com by disabling your adblocker.