Solve Using the Square Root Property (6d+1)^2+12=13

${(6 d + 1)}^{2} + 12 = 13$

Step 1

Subtract $12$ from both sides of the equation.

${(6 d + 1)}^{2} = 13 - 12$

Step 2

Subtract $12$ from $13$ .

${(6 d + 1)}^{2} = 1$

Step 3

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

$6 d + 1 = \pm \sqrt{1}$

Step 4

Any root of $1$ is $1$ .

$6 d + 1 = \pm 1$

Step 5

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.

$6 d + 1 = 1$

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

Subtract $1$ from both sides of the equation.

$6 d = 1 - 1$

Subtract $1$ from $1$ .

$6 d = 0$

Divide each term in $6 d = 0$ by $6$ and simplify.

Divide each term in $6 d = 0$ by $6$ .

$\frac{6 d}{6} = \frac{0}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 d}{6} = \frac{0}{6}$

Divide $d$ by $1$ .

$d = \frac{0}{6}$

Simplify the right side.

Divide $0$ by $6$ .

$d = 0$

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

$6 d + 1 = - 1$

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

Subtract $1$ from both sides of the equation.

$6 d = - 1 - 1$

Subtract $1$ from $- 1$ .

$6 d = - 2$

Divide each term in $6 d = - 2$ by $6$ and simplify.

Divide each term in $6 d = - 2$ by $6$ .

$\frac{6 d}{6} = \frac{- 2}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 d}{6} = \frac{- 2}{6}$

Divide $d$ by $1$ .

$d = \frac{- 2}{6}$

Simplify the right side.

Cancel the common factor of $- 2$ and $6$ .

Factor $2$ out of $- 2$ .

$d = \frac{2 (- 1)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$d = \frac{2 \cdot - 1}{2 \cdot 3}$

Cancel the common factor.

$d = \frac{2 \cdot - 1}{2 \cdot 3}$

Rewrite the expression.

$d = \frac{- 1}{3}$

Move the negative in front of the fraction.

$d = - \frac{1}{3}$

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

$d = 0, - \frac{1}{3}$

Solve Using the Square Root Property (6d+1)^2+12=13

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