Algebra Examples

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

Step 1

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

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Step 1.1

Add $5$ to both sides of the equation.

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

Step 1.2

Add $2$ and $5$ .

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

Step 2

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

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

Step 3

Simplify each side of the equation.

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

Combine fractions.

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Step 3.2.1.1.1

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

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

Step 3.2.1.1.2

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

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

Step 3.2.1.2

Simplify the numerator.

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Step 3.2.1.2.1

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

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Step 3.2.1.2.1.1

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

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

Step 3.2.1.2.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.2.1.2.1

Cancel the common factor.

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

Step 3.2.1.2.1.2.2

Rewrite the expression.

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

Step 3.2.1.2.2

Simplify.

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

Step 3.2.1.3

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

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

Step 3.3

Simplify the right side.

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Step 3.3.1

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

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

Step 4

Solve for $x$ .

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Step 4.1

Multiply both sides of the equation by $4$ .

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

Step 4.2

Simplify both sides of the equation.

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Cancel the common factor of $4$ .

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Step 4.2.1.1.1

Cancel the common factor.

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

Step 4.2.1.1.2

Rewrite the expression.

$x = 4 \cdot 49$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Multiply $4$ by $49$ .

$x = 196$