Algebra Examples

$\sqrt{4 x + 28} - 3 \sqrt{2 x} = 0$

Step 1

Add $3 \sqrt{2 x}$ to both sides of the equation.

$\sqrt{4 x + 28} = 3 \sqrt{2 x}$

Step 2

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

${\sqrt{4 x + 28}}^{2} = {(3 \sqrt{2 x})}^{2}$

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 $\sqrt{4 x + 28}$ as ${(4 x + 28)}^{\frac{1}{2}}$ .

${({(4 x + 28)}^{\frac{1}{2}})}^{2} = {(3 \sqrt{2 x})}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(4 x + 28)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(4 x + 28)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(4 x + 28)}^{\frac{1}{2} \cdot 2} = {(3 \sqrt{2 x})}^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(4 x + 28)}^{\frac{1}{2} \cdot 2} = {(3 \sqrt{2 x})}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(4 x + 28)}^{1} = {(3 \sqrt{2 x})}^{2}$

Step 3.2.1.2

Simplify.

$4 x + 28 = {(3 \sqrt{2 x})}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(3 \sqrt{2 x})}^{2}$ .

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Step 3.3.1.1

Simplify the expression.

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Step 3.3.1.1.1

Apply the product rule to $3 \sqrt{2 x}$ .

$4 x + 28 = 3^{2} {\sqrt{2 x}}^{2}$

Step 3.3.1.1.2

Raise $3$ to the power of $2$ .

$4 x + 28 = 9 {\sqrt{2 x}}^{2}$

Step 3.3.1.2

Rewrite ${\sqrt{2 x}}^{2}$ as $2 x$ .

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Step 3.3.1.2.1

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

$4 x + 28 = 9 {({(2 x)}^{\frac{1}{2}})}^{2}$

Step 3.3.1.2.2

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

$4 x + 28 = 9 {(2 x)}^{\frac{1}{2} \cdot 2}$

Step 3.3.1.2.3

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

$4 x + 28 = 9 {(2 x)}^{\frac{2}{2}}$

Step 3.3.1.2.4

Cancel the common factor of $2$ .

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Step 3.3.1.2.4.1

Cancel the common factor.

$4 x + 28 = 9 {(2 x)}^{\frac{2}{2}}$

Step 3.3.1.2.4.2

Rewrite the expression.

$4 x + 28 = 9 {(2 x)}^{1}$

Step 3.3.1.2.5

Simplify.

$4 x + 28 = 9 (2 x)$

Step 3.3.1.3

Multiply $2$ by $9$ .

$4 x + 28 = 18 x$

Step 4

Solve for $x$ .

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Step 4.1

Move all terms containing $x$ to the left side of the equation.

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Step 4.1.1

Subtract $18 x$ from both sides of the equation.

$4 x + 28 - 18 x = 0$

Step 4.1.2

Subtract $18 x$ from $4 x$ .

$- 14 x + 28 = 0$

Step 4.2

Subtract $28$ from both sides of the equation.

$- 14 x = - 28$

Step 4.3

Divide each term in $- 14 x = - 28$ by $- 14$ and simplify.

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Step 4.3.1

Divide each term in $- 14 x = - 28$ by $- 14$ .

$\frac{- 14 x}{- 14} = \frac{- 28}{- 14}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 14$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 14 x}{- 14} = \frac{- 28}{- 14}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 28}{- 14}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $- 28$ by $- 14$ .

$x = 2$