Solve for x 6 square root of 3x+2=14

$6 \sqrt{3 x} + 2 = 14$

Step 1

Move all terms not containing $6 \sqrt{3 x}$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$6 \sqrt{3 x} = 14 - 2$

Subtract $2$ from $14$ .

$6 \sqrt{3 x} = 12$

Step 2

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

${(6 \sqrt{3 x})}^{2} = 12^{2}$

Step 3

Simplify each side of the equation.

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

${(6 {(3 x)}^{\frac{1}{2}})}^{2} = 12^{2}$

Simplify the left side.

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

Apply the product rule to $3 x$ .

${(6 (3^{\frac{1}{2}} x^{\frac{1}{2}}))}^{2} = 12^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $6 \cdot 3^{\frac{1}{2}} x^{\frac{1}{2}}$ .

${(6 \cdot 3^{\frac{1}{2}})}^{2} {(x^{\frac{1}{2}})}^{2} = 12^{2}$

Apply the product rule to $6 \cdot 3^{\frac{1}{2}}$ .

$6^{2} \cdot {(3^{\frac{1}{2}})}^{2} {(x^{\frac{1}{2}})}^{2} = 12^{2}$

Raise $6$ to the power of $2$ .

$36 \cdot {(3^{\frac{1}{2}})}^{2} {(x^{\frac{1}{2}})}^{2} = 12^{2}$

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

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

$36 \cdot 3^{\frac{1}{2} \cdot 2} {(x^{\frac{1}{2}})}^{2} = 12^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$36 \cdot 3^{\frac{1}{2} \cdot 2} {(x^{\frac{1}{2}})}^{2} = 12^{2}$

Rewrite the expression.

$36 \cdot 3^{1} {(x^{\frac{1}{2}})}^{2} = 12^{2}$

Evaluate the exponent.

$36 \cdot 3 {(x^{\frac{1}{2}})}^{2} = 12^{2}$

Multiply $36$ by $3$ .

$108 {(x^{\frac{1}{2}})}^{2} = 12^{2}$

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

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

$108 x^{\frac{1}{2} \cdot 2} = 12^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$108 x^{\frac{1}{2} \cdot 2} = 12^{2}$

Rewrite the expression.

$108 x^{1} = 12^{2}$

Simplify.

$108 x = 12^{2}$

Simplify the right side.

Raise $12$ to the power of $2$ .

$108 x = 144$

Step 4

Divide each term in $108 x = 144$ by $108$ and simplify.

Divide each term in $108 x = 144$ by $108$ .

$\frac{108 x}{108} = \frac{144}{108}$

Simplify the left side.

Cancel the common factor of $108$ .

Cancel the common factor.

$\frac{108 x}{108} = \frac{144}{108}$

Divide $x$ by $1$ .

$x = \frac{144}{108}$

Simplify the right side.

Cancel the common factor of $144$ and $108$ .

Factor $36$ out of $144$ .

$x = \frac{36 (4)}{108}$

Cancel the common factors.

Factor $36$ out of $108$ .

$x = \frac{36 \cdot 4}{36 \cdot 3}$

Cancel the common factor.

$x = \frac{36 \cdot 4}{36 \cdot 3}$

Rewrite the expression.

$x = \frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{3}$

Decimal Form:

$x = 1.\overline{3}$

Mixed Number Form:

$x = 1 \frac{1}{3}$

Solve for x 6 square root of 3x+2=14

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