Solve for x 1/2 square root of x-5=2

$\frac{1}{2} \sqrt{x} - 5 = 2$

Move all terms not containing $\frac{1}{2} \cdot \sqrt{x}$ to the right side of the equation.

Add $5$ to both sides of the equation.

$\frac{1}{2} \cdot \sqrt{x} = 2 + 5$

Add $2$ and $5$ .

$\frac{1}{2} \cdot \sqrt{x} = 7$

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

${(\frac{1}{2} \cdot \sqrt{x})}^{2} = 7^{2}$

Simplify each side of the equation.

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

${(\frac{1}{2} \cdot x^{\frac{1}{2}})}^{2} = 7^{2}$

Simplify the left side.

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

Combine fractions.

Combine $\frac{1}{2}$ and $x^{\frac{1}{2}}$ .

${(\frac{x^{\frac{1}{2}}}{2})}^{2} = 7^{2}$

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

$\frac{{(x^{\frac{1}{2}})}^{2}}{2^{2}} = 7^{2}$

Simplify the numerator.

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

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

$\frac{x^{\frac{1}{2} \cdot 2}}{2^{2}} = 7^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x^{\frac{1}{2} \cdot 2}}{2^{2}} = 7^{2}$

Rewrite the expression.

$\frac{x^{1}}{2^{2}} = 7^{2}$

Simplify.

$\frac{x}{2^{2}} = 7^{2}$

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

$\frac{x}{4} = 7^{2}$

Simplify the right side.

Raise $7$ to the power of $2$ .

$\frac{x}{4} = 49$

Solve for $x$ .

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 \cdot 49$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{x}{4} = 4 \cdot 49$

Rewrite the expression.

$x = 4 \cdot 49$

Simplify the right side.

Multiply $4$ by $49$ .

$x = 196$

Solve for x 1/2 square root of x-5=2

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