Solve for x square root of 6-3x-2=0

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

Step 1

Add $2$ to both sides of the equation.

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

Step 2

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

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

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 - 3 x}$ as ${(6 - 3 x)}^{\frac{1}{2}}$ .

${({(6 - 3 x)}^{\frac{1}{2}})}^{2} = 2^{2}$

Simplify the left side.

Simplify ${({(6 - 3 x)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(6 - 3 x)}^{\frac{1}{2}})}^{2}$ .

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

${(6 - 3 x)}^{\frac{1}{2} \cdot 2} = 2^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(6 - 3 x)}^{\frac{1}{2} \cdot 2} = 2^{2}$

Rewrite the expression.

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

Simplify.

$6 - 3 x = 2^{2}$

Simplify the right side.

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

$6 - 3 x = 4$

Step 4

Solve for $x$ .

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

Subtract $6$ from both sides of the equation.

$- 3 x = 4 - 6$

Subtract $6$ from $4$ .

$- 3 x = - 2$

Divide each term in $- 3 x = - 2$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 2$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 2}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 2}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 3}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{2}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{3}$

Decimal Form:

$x = 0.\overline{6}$

Solve for x square root of 6-3x-2=0

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