Algebra Examples

$A = 6 {(s + 2)}^{2}$

Step 1

Rewrite the equation as $6 {(s + 2)}^{2} = A$ .

$6 {(s + 2)}^{2} = A$

Step 2

Divide each term in $6 {(s + 2)}^{2} = A$ by $6$ and simplify.

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Step 2.1

Divide each term in $6 {(s + 2)}^{2} = A$ by $6$ .

$\frac{6 {(s + 2)}^{2}}{6} = \frac{A}{6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 {(s + 2)}^{2}}{6} = \frac{A}{6}$

Step 2.2.1.2

Divide ${(s + 2)}^{2}$ by $1$ .

${(s + 2)}^{2} = \frac{A}{6}$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$s + 2 = \pm \sqrt{\frac{A}{6}}$

Step 4

Simplify $\pm \sqrt{\frac{A}{6}}$ .

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Step 4.1

Rewrite $\sqrt{\frac{A}{6}}$ as $\frac{\sqrt{A}}{\sqrt{6}}$ .

$s + 2 = \pm \frac{\sqrt{A}}{\sqrt{6}}$

Step 4.2

Multiply $\frac{\sqrt{A}}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$s + 2 = \pm \frac{\sqrt{A}}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}}$

Step 4.3

Combine and simplify the denominator.

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Step 4.3.1

Multiply $\frac{\sqrt{A}}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$s + 2 = \pm \frac{\sqrt{A} \sqrt{6}}{\sqrt{6} \sqrt{6}}$

Step 4.3.2

Raise $\sqrt{6}$ to the power of $1$ .

$s + 2 = \pm \frac{\sqrt{A} \sqrt{6}}{{\sqrt{6}}^{1} \sqrt{6}}$

Step 4.3.3

Raise $\sqrt{6}$ to the power of $1$ .

$s + 2 = \pm \frac{\sqrt{A} \sqrt{6}}{{\sqrt{6}}^{1} {\sqrt{6}}^{1}}$

Step 4.3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$s + 2 = \pm \frac{\sqrt{A} \sqrt{6}}{{\sqrt{6}}^{1 + 1}}$

Step 4.3.5

Add $1$ and $1$ .

$s + 2 = \pm \frac{\sqrt{A} \sqrt{6}}{{\sqrt{6}}^{2}}$

Step 4.3.6

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

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Step 4.3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$s + 2 = \pm \frac{\sqrt{A} \sqrt{6}}{{(6^{\frac{1}{2}})}^{2}}$

Step 4.3.6.2

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

$s + 2 = \pm \frac{\sqrt{A} \sqrt{6}}{6^{\frac{1}{2} \cdot 2}}$

Step 4.3.6.3

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

$s + 2 = \pm \frac{\sqrt{A} \sqrt{6}}{6^{\frac{2}{2}}}$

Step 4.3.6.4

Cancel the common factor of $2$ .

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Step 4.3.6.4.1

Cancel the common factor.

$s + 2 = \pm \frac{\sqrt{A} \sqrt{6}}{6^{\frac{2}{2}}}$

Step 4.3.6.4.2

Rewrite the expression.

$s + 2 = \pm \frac{\sqrt{A} \sqrt{6}}{6^{1}}$

Step 4.3.6.5

Evaluate the exponent.

$s + 2 = \pm \frac{\sqrt{A} \sqrt{6}}{6}$

Step 4.4

Combine using the product rule for radicals.

$s + 2 = \pm \frac{\sqrt{A \cdot 6}}{6}$

Step 4.5

Reorder factors in $\pm \frac{\sqrt{A \cdot 6}}{6}$ .

$s + 2 = \pm \frac{\sqrt{6 A}}{6}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$s + 2 = \frac{\sqrt{6 A}}{6}$

Step 5.2

Subtract $2$ from both sides of the equation.

$s = \frac{\sqrt{6 A}}{6} - 2$

Step 5.3

Next, use the negative value of the $\pm$ to find the second solution.

$s + 2 = - \frac{\sqrt{6 A}}{6}$

Step 5.4

Subtract $2$ from both sides of the equation.

$s = - \frac{\sqrt{6 A}}{6} - 2$

Step 5.5

The complete solution is the result of both the positive and negative portions of the solution.

$s = \frac{\sqrt{6 A}}{6} - 2$

$s = - \frac{\sqrt{6 A}}{6} - 2$

$s = \frac{\sqrt{6 A}}{6} - 2$

$s = - \frac{\sqrt{6 A}}{6} - 2$