Algebra Examples

$\sqrt{9 (x - 1)} = 21$

Step 1

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

${\sqrt{9 (x - 1)}}^{2} = 21^{2}$

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 $\sqrt{9 (x - 1)}$ as ${(9 (x - 1))}^{\frac{1}{2}}$ .

${({(9 (x - 1))}^{\frac{1}{2}})}^{2} = 21^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(9 (x - 1))}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(9 (x - 1))}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

${(9 (x - 1))}^{\frac{1}{2} \cdot 2} = 21^{2}$

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.

${(9 (x - 1))}^{\frac{1}{2} \cdot 2} = 21^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(9 (x - 1))}^{1} = 21^{2}$

Step 2.2.1.2

Apply the distributive property.

${(9 x + 9 \cdot - 1)}^{1} = 21^{2}$

Step 2.2.1.3

Multiply.

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Step 2.2.1.3.1

Multiply $9$ by $- 1$ .

${(9 x - 9)}^{1} = 21^{2}$

Step 2.2.1.3.2

Simplify.

$9 x - 9 = 21^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $21$ to the power of $2$ .

$9 x - 9 = 441$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $9$ to both sides of the equation.

$9 x = 441 + 9$

Step 3.1.2

Add $441$ and $9$ .

$9 x = 450$

Step 3.2

Divide each term in $9 x = 450$ by $9$ and simplify.

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Step 3.2.1

Divide each term in $9 x = 450$ by $9$ .

$\frac{9 x}{9} = \frac{450}{9}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $9$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{450}{9}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{450}{9}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $450$ by $9$ .

$x = 50$