Algebra Examples

$\sqrt{x - 4} = 5$

Step 1

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

${\sqrt{x - 4}}^{2} = 5^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 4}$ as ${(x - 4)}^{\frac{1}{2}}$ .

${({(x - 4)}^{\frac{1}{2}})}^{2} = 5^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(x - 4)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(x - 4)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

${(x - 4)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(x - 4)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(x - 4)}^{1} = 5^{2}$

Step 2.2.1.2

Simplify.

$x - 4 = 5^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $5$ to the power of $2$ .

$x - 4 = 25$

Step 3

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

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Step 3.1

Add $4$ to both sides of the equation.

$x = 25 + 4$

Step 3.2

Add $25$ and $4$ .

$x = 29$