Solve Using the Square Root Property (6y+13)^2=50

${(6 y + 13)}^{2} = 50$

Step 1

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

$6 y + 13 = \pm \sqrt{50}$

Step 2

Simplify $\pm \sqrt{50}$ .

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$6 y + 13 = \pm \sqrt{25 (2)}$

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

$6 y + 13 = \pm \sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$6 y + 13 = \pm 5 \sqrt{2}$

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.

$6 y + 13 = 5 \sqrt{2}$

Subtract $13$ from both sides of the equation.

$6 y = 5 \sqrt{2} - 13$

Divide each term in $6 y = 5 \sqrt{2} - 13$ by $6$ and simplify.

Divide each term in $6 y = 5 \sqrt{2} - 13$ by $6$ .

$\frac{6 y}{6} = \frac{5 \sqrt{2}}{6} + \frac{- 13}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{5 \sqrt{2}}{6} + \frac{- 13}{6}$

Divide $y$ by $1$ .

$y = \frac{5 \sqrt{2}}{6} + \frac{- 13}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{5 \sqrt{2}}{6} - \frac{13}{6}$

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

$6 y + 13 = - 5 \sqrt{2}$

Subtract $13$ from both sides of the equation.

$6 y = - 5 \sqrt{2} - 13$

Divide each term in $6 y = - 5 \sqrt{2} - 13$ by $6$ and simplify.

Divide each term in $6 y = - 5 \sqrt{2} - 13$ by $6$ .

$\frac{6 y}{6} = \frac{- 5 \sqrt{2}}{6} + \frac{- 13}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 5 \sqrt{2}}{6} + \frac{- 13}{6}$

Divide $y$ by $1$ .

$y = \frac{- 5 \sqrt{2}}{6} + \frac{- 13}{6}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{5 \sqrt{2}}{6} + \frac{- 13}{6}$

Move the negative in front of the fraction.

$y = - \frac{5 \sqrt{2}}{6} - \frac{13}{6}$

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

$y = \frac{5 \sqrt{2}}{6} - \frac{13}{6}, - \frac{5 \sqrt{2}}{6} - \frac{13}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{5 \sqrt{2}}{6} - \frac{13}{6}, - \frac{5 \sqrt{2}}{6} - \frac{13}{6}$

Decimal Form:

$y = - 0.98815536 \dots, - 3.34517796 \dots$

Solve Using the Square Root Property (6y+13)^2=50

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