Solve Using the Square Root Property (3x+1)^2=6

${(3 x + 1)}^{2} = 6$

Step 1

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

$3 x + 1 = \pm \sqrt{6}$

Step 2

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.

$3 x + 1 = \sqrt{6}$

Subtract $1$ from both sides of the equation.

$3 x = \sqrt{6} - 1$

Divide each term in $3 x = \sqrt{6} - 1$ by $3$ and simplify.

Divide each term in $3 x = \sqrt{6} - 1$ by $3$ .

$\frac{3 x}{3} = \frac{\sqrt{6}}{3} + \frac{- 1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{\sqrt{6}}{3} + \frac{- 1}{3}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{6}}{3} + \frac{- 1}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{\sqrt{6}}{3} - \frac{1}{3}$

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

$3 x + 1 = - \sqrt{6}$

Subtract $1$ from both sides of the equation.

$3 x = - \sqrt{6} - 1$

Divide each term in $3 x = - \sqrt{6} - 1$ by $3$ and simplify.

Divide each term in $3 x = - \sqrt{6} - 1$ by $3$ .

$\frac{3 x}{3} = \frac{- \sqrt{6}}{3} + \frac{- 1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- \sqrt{6}}{3} + \frac{- 1}{3}$

Divide $x$ by $1$ .

$x = \frac{- \sqrt{6}}{3} + \frac{- 1}{3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{\sqrt{6}}{3} + \frac{- 1}{3}$

Move the negative in front of the fraction.

$x = - \frac{\sqrt{6}}{3} - \frac{1}{3}$

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

$x = \frac{\sqrt{6}}{3} - \frac{1}{3}, - \frac{\sqrt{6}}{3} - \frac{1}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{6}}{3} - \frac{1}{3}, - \frac{\sqrt{6}}{3} - \frac{1}{3}$

Decimal Form:

$x = 0.48316324 \dots, - 1.14982991 \dots$

Solve Using the Square Root Property (3x+1)^2=6

Related Questions

Support LCMGCF.com by disabling your adblocker.