Solve by Factoring -2+ square root of 3x-2=6

$- 2 + \sqrt{3 x - 2} = 6$

Step 1

Subtract $6$ from both sides of the equation.

$- 2 + \sqrt{3 x - 2} - 6 = 0$

Step 2

Subtract $6$ from $- 2$ .

$- 8 + \sqrt{3 x - 2} = 0$

Step 3

Add $8$ to both sides of the equation.

$\sqrt{3 x - 2} = 8$

Step 4

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{3 x - 2}}^{2} = 8^{2}$

Step 5

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 2}$ as ${(3 x - 2)}^{\frac{1}{2}}$ .

${({(3 x - 2)}^{\frac{1}{2}})}^{2} = 8^{2}$

Simplify the left side.

Simplify ${({(3 x - 2)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 x - 2)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(3 x - 2)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x - 2)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Rewrite the expression.

${(3 x - 2)}^{1} = 8^{2}$

Simplify.

$3 x - 2 = 8^{2}$

Simplify the right side.

Raise $8$ to the power of $2$ .

$3 x - 2 = 64$

Step 6

Solve for $x$ .

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

Add $2$ to both sides of the equation.

$3 x = 64 + 2$

Add $64$ and $2$ .

$3 x = 66$

Divide each term in $3 x = 66$ by $3$ and simplify.

Divide each term in $3 x = 66$ by $3$ .

$\frac{3 x}{3} = \frac{66}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{66}{3}$

Divide $x$ by $1$ .

$x = \frac{66}{3}$

Simplify the right side.

Divide $66$ by $3$ .

$x = 22$

Solve by Factoring -2+ square root of 3x-2=6

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