Solve for x ( square root of 2x)/4+3=5

$\frac{\sqrt{2 x}}{4} + 3 = 5$

Step 1

Solve for $\sqrt{2 x}$ .

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

Subtract $3$ from both sides of the equation.

$\frac{\sqrt{2 x}}{4} = 5 - 3$

Subtract $3$ from $5$ .

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

Multiply both sides of the equation by $4$ .

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

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Multiply $4$ by $2$ .

$\sqrt{2 x} = 8$

Step 2

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

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

Step 3

Simplify each side of the equation.

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

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

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, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$2 x = 8^{2}$

Simplify the right side.

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

$2 x = 64$

Step 4

Divide each term in $2 x = 64$ by $2$ and simplify.

Divide each term in $2 x = 64$ by $2$ .

$\frac{2 x}{2} = \frac{64}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{64}{2}$

Divide $x$ by $1$ .

$x = \frac{64}{2}$

Simplify the right side.

Divide $64$ by $2$ .

$x = 32$

Solve for x ( square root of 2x)/4+3=5

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