Solve by Factoring 4+ square root of 6x+4=8

$4 + \sqrt{6 x + 4} = 8$

Step 1

Subtract $8$ from both sides of the equation.

$4 + \sqrt{6 x + 4} - 8 = 0$

Step 2

Simplify $4 + \sqrt{6 x + 4} - 8$ .

Factor $2$ out of $6 x + 4$ .

Factor $2$ out of $6 x$ .

$4 + \sqrt{2 (3 x) + 4} - 8 = 0$

Factor $2$ out of $4$ .

$4 + \sqrt{2 (3 x) + 2 (2)} - 8 = 0$

Factor $2$ out of $2 (3 x) + 2 (2)$ .

$4 + \sqrt{2 (3 x + 2)} - 8 = 0$

Subtract $8$ from $4$ .

$- 4 + \sqrt{2 (3 x + 2)} = 0$

Step 3

Add $4$ to both sides of the equation.

$\sqrt{2 (3 x + 2)} = 4$

Step 4

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

${\sqrt{2 (3 x + 2)}}^{2} = 4^{2}$

Step 5

Simplify each side of the equation.

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

${({(2 (3 x + 2))}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

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

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

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

${(2 (3 x + 2))}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 (3 x + 2))}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(2 (3 x + 2))}^{1} = 4^{2}$

Apply the distributive property.

${(2 (3 x) + 2 \cdot 2)}^{1} = 4^{2}$

Multiply.

Multiply $3$ by $2$ .

${(6 x + 2 \cdot 2)}^{1} = 4^{2}$

Multiply $2$ by $2$ .

${(6 x + 4)}^{1} = 4^{2}$

Simplify.

$6 x + 4 = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$6 x + 4 = 16$

Step 6

Solve for $x$ .

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

Subtract $4$ from both sides of the equation.

$6 x = 16 - 4$

Subtract $4$ from $16$ .

$6 x = 12$

Divide each term in $6 x = 12$ by $6$ and simplify.

Divide each term in $6 x = 12$ by $6$ .

$\frac{6 x}{6} = \frac{12}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{12}{6}$

Divide $x$ by $1$ .

$x = \frac{12}{6}$

Simplify the right side.

Divide $12$ by $6$ .

$x = 2$

Solve by Factoring 4+ square root of 6x+4=8

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