Algebra Examples

$2 \sqrt{x + 1} = 14$

Step 1

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

${(2 \sqrt{x + 1})}^{2} = 14^{2}$

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

${(2 {(x + 1)}^{\frac{1}{2}})}^{2} = 14^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

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

$2^{2} {({(x + 1)}^{\frac{1}{2}})}^{2} = 14^{2}$

Step 2.2.1.2

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

$4 {({(x + 1)}^{\frac{1}{2}})}^{2} = 14^{2}$

Step 2.2.1.3

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

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Step 2.2.1.3.1

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

$4 {(x + 1)}^{\frac{1}{2} \cdot 2} = 14^{2}$

Step 2.2.1.3.2

Cancel the common factor of $2$ .

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Step 2.2.1.3.2.1

Cancel the common factor.

$4 {(x + 1)}^{\frac{1}{2} \cdot 2} = 14^{2}$

Step 2.2.1.3.2.2

Rewrite the expression.

$4 {(x + 1)}^{1} = 14^{2}$

Step 2.2.1.4

Simplify.

$4 (x + 1) = 14^{2}$

Step 2.2.1.5

Apply the distributive property.

$4 x + 4 \cdot 1 = 14^{2}$

Step 2.2.1.6

Multiply $4$ by $1$ .

$4 x + 4 = 14^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $14$ to the power of $2$ .

$4 x + 4 = 196$

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

Subtract $4$ from both sides of the equation.

$4 x = 196 - 4$

Step 3.1.2

Subtract $4$ from $196$ .

$4 x = 192$

Step 3.2

Divide each term in $4 x = 192$ by $4$ and simplify.

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Step 3.2.1

Divide each term in $4 x = 192$ by $4$ .

$\frac{4 x}{4} = \frac{192}{4}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{192}{4}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{192}{4}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $192$ by $4$ .

$x = 48$