Solve Using the Square Root Property 3(2b+3)^2=36

$3 {(2 b + 3)}^{2} = 36$

Step 1

Divide each term in $3 {(2 b + 3)}^{2} = 36$ by $3$ and simplify.

Divide each term in $3 {(2 b + 3)}^{2} = 36$ by $3$ .

$\frac{3 {(2 b + 3)}^{2}}{3} = \frac{36}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 {(2 b + 3)}^{2}}{3} = \frac{36}{3}$

Divide ${(2 b + 3)}^{2}$ by $1$ .

${(2 b + 3)}^{2} = \frac{36}{3}$

Simplify the right side.

Divide $36$ by $3$ .

${(2 b + 3)}^{2} = 12$

Step 2

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

$2 b + 3 = \pm \sqrt{12}$

Step 3

Simplify $\pm \sqrt{12}$ .

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$2 b + 3 = \pm \sqrt{4 (3)}$

Rewrite $4$ as $2^{2}$ .

$2 b + 3 = \pm \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$2 b + 3 = \pm 2 \sqrt{3}$

Step 4

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.

$2 b + 3 = 2 \sqrt{3}$

Subtract $3$ from both sides of the equation.

$2 b = 2 \sqrt{3} - 3$

Divide each term in $2 b = 2 \sqrt{3} - 3$ by $2$ and simplify.

Divide each term in $2 b = 2 \sqrt{3} - 3$ by $2$ .

$\frac{2 b}{2} = \frac{2 \sqrt{3}}{2} + \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 b}{2} = \frac{2 \sqrt{3}}{2} + \frac{- 3}{2}$

Divide $b$ by $1$ .

$b = \frac{2 \sqrt{3}}{2} + \frac{- 3}{2}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

$b = \frac{2 \sqrt{3}}{2} + \frac{- 3}{2}$

Divide $\sqrt{3}$ by $1$ .

$b = \sqrt{3} + \frac{- 3}{2}$

Move the negative in front of the fraction.

$b = \sqrt{3} - \frac{3}{2}$

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

$2 b + 3 = - 2 \sqrt{3}$

Subtract $3$ from both sides of the equation.

$2 b = - 2 \sqrt{3} - 3$

Divide each term in $2 b = - 2 \sqrt{3} - 3$ by $2$ and simplify.

Divide each term in $2 b = - 2 \sqrt{3} - 3$ by $2$ .

$\frac{2 b}{2} = \frac{- 2 \sqrt{3}}{2} + \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 b}{2} = \frac{- 2 \sqrt{3}}{2} + \frac{- 3}{2}$

Divide $b$ by $1$ .

$b = \frac{- 2 \sqrt{3}}{2} + \frac{- 3}{2}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $- 2 \sqrt{3}$ .

$b = \frac{2 (- \sqrt{3})}{2} + \frac{- 3}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$b = \frac{2 (- \sqrt{3})}{2 (1)} + \frac{- 3}{2}$

Cancel the common factor.

$b = \frac{2 (- \sqrt{3})}{2 \cdot 1} + \frac{- 3}{2}$

Rewrite the expression.

$b = \frac{- \sqrt{3}}{1} + \frac{- 3}{2}$

Divide $- \sqrt{3}$ by $1$ .

$b = - \sqrt{3} + \frac{- 3}{2}$

Move the negative in front of the fraction.

$b = - \sqrt{3} - \frac{3}{2}$

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

$b = \sqrt{3} - \frac{3}{2}, - \sqrt{3} - \frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = \sqrt{3} - \frac{3}{2}, - \sqrt{3} - \frac{3}{2}$

Decimal Form:

$b = 0.23205080 \dots, - 3.23205080 \dots$

Solve Using the Square Root Property 3(2b+3)^2=36

Related Questions

Support LCMGCF.com by disabling your adblocker.