Algebra Examples

$- 2 \sqrt{6 x + 3} = - 18$

Step 1

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

${(- 2 \sqrt{6 x + 3})}^{2} = {(- 18)}^{2}$

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 $\sqrt{6 x + 3}$ as ${(6 x + 3)}^{\frac{1}{2}}$ .

${(- 2 {(6 x + 3)}^{\frac{1}{2}})}^{2} = {(- 18)}^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${(- 2 {(6 x + 3)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Apply the product rule to $- 2 {(6 x + 3)}^{\frac{1}{2}}$ .

${(- 2)}^{2} {({(6 x + 3)}^{\frac{1}{2}})}^{2} = {(- 18)}^{2}$

Step 2.2.1.2

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

$4 {({(6 x + 3)}^{\frac{1}{2}})}^{2} = {(- 18)}^{2}$

Step 2.2.1.3

Multiply the exponents in ${({(6 x + 3)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.3.1

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

$4 {(6 x + 3)}^{\frac{1}{2} \cdot 2} = {(- 18)}^{2}$

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.

$4 {(6 x + 3)}^{\frac{1}{2} \cdot 2} = {(- 18)}^{2}$

Step 2.2.1.3.2.2

Rewrite the expression.

$4 {(6 x + 3)}^{1} = {(- 18)}^{2}$

Step 2.2.1.4

Simplify.

$4 (6 x + 3) = {(- 18)}^{2}$

Step 2.2.1.5

Apply the distributive property.

$4 (6 x) + 4 \cdot 3 = {(- 18)}^{2}$

Step 2.2.1.6

Multiply.

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Step 2.2.1.6.1

Multiply $6$ by $4$ .

$24 x + 4 \cdot 3 = {(- 18)}^{2}$

Step 2.2.1.6.2

Multiply $4$ by $3$ .

$24 x + 12 = {(- 18)}^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $- 18$ to the power of $2$ .

$24 x + 12 = 324$

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 $12$ from both sides of the equation.

$24 x = 324 - 12$

Step 3.1.2

Subtract $12$ from $324$ .

$24 x = 312$

Step 3.2

Divide each term in $24 x = 312$ by $24$ and simplify.

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Step 3.2.1

Divide each term in $24 x = 312$ by $24$ .

$\frac{24 x}{24} = \frac{312}{24}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $24$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{24 x}{24} = \frac{312}{24}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{312}{24}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $312$ by $24$ .

$x = 13$