Solve for x ( square root of 2x+2)/4=3

$\frac{\sqrt{2 x} + 2}{4} = 3$

Step 1

Multiply both sides by $4$ .

$\frac{\sqrt{2 x} + 2}{4} \cdot 4 = 3 \cdot 4$

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{\sqrt{2 x} + 2}{4} \cdot 4 = 3 \cdot 4$

Rewrite the expression.

$\sqrt{2 x} + 2 = 3 \cdot 4$

Simplify the right side.

Multiply $3$ by $4$ .

$\sqrt{2 x} + 2 = 12$

Step 3

Solve for $x$ .

Move all terms not containing $\sqrt{2 x}$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$\sqrt{2 x} = 12 - 2$

Subtract $2$ from $12$ .

$\sqrt{2 x} = 10$

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

${\sqrt{2 x}}^{2} = 10^{2}$

Simplify each side of the equation.

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

${({(2 x)}^{\frac{1}{2}})}^{2} = 10^{2}$

Simplify the left side.

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

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

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

${(2 x)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Rewrite the expression.

${(2 x)}^{1} = 10^{2}$

Simplify.

$2 x = 10^{2}$

Simplify the right side.

Raise $10$ to the power of $2$ .

$2 x = 100$

Divide each term in $2 x = 100$ by $2$ and simplify.

Divide each term in $2 x = 100$ by $2$ .

$\frac{2 x}{2} = \frac{100}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{100}{2}$

Divide $x$ by $1$ .

$x = \frac{100}{2}$

Simplify the right side.

Divide $100$ by $2$ .

$x = 50$

Solve for x ( square root of 2x+2)/4=3

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