Algebra Examples

$\sqrt{- 5 - b} = \sqrt{5 b + 25}$

Step 1

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

${\sqrt{- 5 - b}}^{2} = {\sqrt{5 b + 25}}^{2}$

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 $\sqrt{- 5 - b}$ as ${(- 5 - b)}^{\frac{1}{2}}$ .

${({(- 5 - b)}^{\frac{1}{2}})}^{2} = {\sqrt{5 b + 25}}^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(- 5 - b)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(- 5 - b)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

${(- 5 - b)}^{\frac{1}{2} \cdot 2} = {\sqrt{5 b + 25}}^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(- 5 - b)}^{\frac{1}{2} \cdot 2} = {\sqrt{5 b + 25}}^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(- 5 - b)}^{1} = {\sqrt{5 b + 25}}^{2}$

Step 2.2.1.2

Simplify.

$- 5 - b = {\sqrt{5 b + 25}}^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify ${\sqrt{5 b + 25}}^{2}$ .

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Step 2.3.1.1

Factor $5$ out of $5 b + 25$ .

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Step 2.3.1.1.1

Factor $5$ out of $5 b$ .

$- 5 - b = {\sqrt{5 (b) + 25}}^{2}$

Step 2.3.1.1.2

Factor $5$ out of $25$ .

$- 5 - b = {\sqrt{5 b + 5 \cdot 5}}^{2}$

Step 2.3.1.1.3

Factor $5$ out of $5 b + 5 \cdot 5$ .

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

Step 2.3.1.2

Rewrite ${\sqrt{5 (b + 5)}}^{2}$ as $5 (b + 5)$ .

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Step 2.3.1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 (b + 5)}$ as ${(5 (b + 5))}^{\frac{1}{2}}$ .

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

Step 2.3.1.2.2

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

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

Step 2.3.1.2.3

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

$- 5 - b = {(5 (b + 5))}^{\frac{2}{2}}$

Step 2.3.1.2.4

Cancel the common factor of $2$ .

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Step 2.3.1.2.4.1

Cancel the common factor.

$- 5 - b = {(5 (b + 5))}^{\frac{2}{2}}$

Step 2.3.1.2.4.2

Rewrite the expression.

$- 5 - b = {(5 (b + 5))}^{1}$

Step 2.3.1.2.5

Simplify.

$- 5 - b = 5 (b + 5)$

Step 2.3.1.3

Apply the distributive property.

$- 5 - b = 5 b + 5 \cdot 5$

Step 2.3.1.4

Multiply $5$ by $5$ .

$- 5 - b = 5 b + 25$

Step 3

Solve for $b$ .

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Step 3.1

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

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Step 3.1.1

Subtract $5 b$ from both sides of the equation.

$- 5 - b - 5 b = 25$

Step 3.1.2

Subtract $5 b$ from $- b$ .

$- 5 - 6 b = 25$

Step 3.2

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

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Step 3.2.1

Add $5$ to both sides of the equation.

$- 6 b = 25 + 5$

Step 3.2.2

Add $25$ and $5$ .

$- 6 b = 30$

Step 3.3

Divide each term in $- 6 b = 30$ by $- 6$ and simplify.

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Step 3.3.1

Divide each term in $- 6 b = 30$ by $- 6$ .

$\frac{- 6 b}{- 6} = \frac{30}{- 6}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 6$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 6 b}{- 6} = \frac{30}{- 6}$

Step 3.3.2.1.2

Divide $b$ by $1$ .

$b = \frac{30}{- 6}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $30$ by $- 6$ .

$b = - 5$