Algebra Examples

$8 - \sqrt{x + 12} = 3$

Step 1

Move all terms not containing $- \sqrt{x + 12}$ to the right side of the equation.

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Step 1.1

Subtract $8$ from both sides of the equation.

$- \sqrt{x + 12} = 3 - 8$

Step 1.2

Subtract $8$ from $3$ .

$- \sqrt{x + 12} = - 5$

Step 2

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

${(- \sqrt{x + 12})}^{2} = {(- 5)}^{2}$

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 $\sqrt{x + 12}$ as ${(x + 12)}^{\frac{1}{2}}$ .

${(- {(x + 12)}^{\frac{1}{2}})}^{2} = {(- 5)}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(- {(x + 12)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Apply the product rule to $- {(x + 12)}^{\frac{1}{2}}$ .

${(- 1)}^{2} {({(x + 12)}^{\frac{1}{2}})}^{2} = {(- 5)}^{2}$

Step 3.2.1.2

Raise $- 1$ to the power of $2$ .

$1 {({(x + 12)}^{\frac{1}{2}})}^{2} = {(- 5)}^{2}$

Step 3.2.1.3

Multiply ${({(x + 12)}^{\frac{1}{2}})}^{2}$ by $1$ .

${({(x + 12)}^{\frac{1}{2}})}^{2} = {(- 5)}^{2}$

Step 3.2.1.4

Multiply the exponents in ${({(x + 12)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.4.1

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

${(x + 12)}^{\frac{1}{2} \cdot 2} = {(- 5)}^{2}$

Step 3.2.1.4.2

Cancel the common factor of $2$ .

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Step 3.2.1.4.2.1

Cancel the common factor.

${(x + 12)}^{\frac{1}{2} \cdot 2} = {(- 5)}^{2}$

Step 3.2.1.4.2.2

Rewrite the expression.

${(x + 12)}^{1} = {(- 5)}^{2}$

Step 3.2.1.5

Simplify.

$x + 12 = {(- 5)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $- 5$ to the power of $2$ .

$x + 12 = 25$

Step 4

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

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Step 4.1

Subtract $12$ from both sides of the equation.

$x = 25 - 12$

Step 4.2

Subtract $12$ from $25$ .

$x = 13$