Pre-Algebra Examples

$2 = 6 \sqrt{5 x + 6}$

Step 1

Rewrite the equation as $6 \sqrt{5 x + 6} = 2$ .

$6 \sqrt{5 x + 6} = 2$

Step 2

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

${(6 \sqrt{5 x + 6})}^{2} = 2^{2}$

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 $\sqrt{5 x + 6}$ as ${(5 x + 6)}^{\frac{1}{2}}$ .

${(6 {(5 x + 6)}^{\frac{1}{2}})}^{2} = 2^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(6 {(5 x + 6)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Apply the product rule to $6 {(5 x + 6)}^{\frac{1}{2}}$ .

$6^{2} {({(5 x + 6)}^{\frac{1}{2}})}^{2} = 2^{2}$

Step 3.2.1.2

Raise $6$ to the power of $2$ .

$36 {({(5 x + 6)}^{\frac{1}{2}})}^{2} = 2^{2}$

Step 3.2.1.3

Multiply the exponents in ${({(5 x + 6)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.3.1

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

$36 {(5 x + 6)}^{\frac{1}{2} \cdot 2} = 2^{2}$

Step 3.2.1.3.2

Cancel the common factor of $2$ .

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Step 3.2.1.3.2.1

Cancel the common factor.

$36 {(5 x + 6)}^{\frac{1}{2} \cdot 2} = 2^{2}$

Step 3.2.1.3.2.2

Rewrite the expression.

$36 {(5 x + 6)}^{1} = 2^{2}$

Step 3.2.1.4

Simplify.

$36 (5 x + 6) = 2^{2}$

Step 3.2.1.5

Apply the distributive property.

$36 (5 x) + 36 \cdot 6 = 2^{2}$

Step 3.2.1.6

Multiply.

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Step 3.2.1.6.1

Multiply $5$ by $36$ .

$180 x + 36 \cdot 6 = 2^{2}$

Step 3.2.1.6.2

Multiply $36$ by $6$ .

$180 x + 216 = 2^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

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

$180 x + 216 = 4$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $216$ from both sides of the equation.

$180 x = 4 - 216$

Step 4.1.2

Subtract $216$ from $4$ .

$180 x = - 212$

Step 4.2

Divide each term in $180 x = - 212$ by $180$ and simplify.

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Step 4.2.1

Divide each term in $180 x = - 212$ by $180$ .

$\frac{180 x}{180} = \frac{- 212}{180}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $180$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{180 x}{180} = \frac{- 212}{180}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 212}{180}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $- 212$ and $180$ .

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Step 4.2.3.1.1

Factor $4$ out of $- 212$ .

$x = \frac{4 (- 53)}{180}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $4$ out of $180$ .

$x = \frac{4 \cdot - 53}{4 \cdot 45}$

Step 4.2.3.1.2.2

Cancel the common factor.

$x = \frac{4 \cdot - 53}{4 \cdot 45}$

Step 4.2.3.1.2.3

Rewrite the expression.

$x = \frac{- 53}{45}$

Step 4.2.3.2

Move the negative in front of the fraction.

$x = - \frac{53}{45}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{53}{45}$

Decimal Form:

$x = - 1.1\overline{7}$

Mixed Number Form:

$x = - 1 \frac{8}{45}$