Algebra Examples

$\sqrt{63 - 7 b - b} = - 9$

Step 1

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

${\sqrt{63 - 7 b - b}}^{2} = {(- 9)}^{2}$

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 $\sqrt{63 - 7 b - b}$ as ${(63 - 7 b - b)}^{\frac{1}{2}}$ .

${({(63 - 7 b - b)}^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(63 - 7 b - b)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(63 - 7 b - b)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

${(63 - 7 b - b)}^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

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.

${(63 - 7 b - b)}^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(63 - 7 b - b)}^{1} = {(- 9)}^{2}$

Step 2.2.1.2

Subtract $b$ from $- 7 b$ .

${(63 - 8 b)}^{1} = {(- 9)}^{2}$

Step 2.2.1.3

Simplify.

$63 - 8 b = {(- 9)}^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $- 9$ to the power of $2$ .

$63 - 8 b = 81$

Step 3

Solve for $b$ .

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Step 3.1

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

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Step 3.1.1

Subtract $63$ from both sides of the equation.

$- 8 b = 81 - 63$

Step 3.1.2

Subtract $63$ from $81$ .

$- 8 b = 18$

Step 3.2

Divide each term in $- 8 b = 18$ by $- 8$ and simplify.

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Step 3.2.1

Divide each term in $- 8 b = 18$ by $- 8$ .

$\frac{- 8 b}{- 8} = \frac{18}{- 8}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 8$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 8 b}{- 8} = \frac{18}{- 8}$

Step 3.2.2.1.2

Divide $b$ by $1$ .

$b = \frac{18}{- 8}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Cancel the common factor of $18$ and $- 8$ .

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Step 3.2.3.1.1

Factor $2$ out of $18$ .

$b = \frac{2 (9)}{- 8}$

Step 3.2.3.1.2

Cancel the common factors.

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Step 3.2.3.1.2.1

Factor $2$ out of $- 8$ .

$b = \frac{2 \cdot 9}{2 \cdot - 4}$

Step 3.2.3.1.2.2

Cancel the common factor.

$b = \frac{2 \cdot 9}{2 \cdot - 4}$

Step 3.2.3.1.2.3

Rewrite the expression.

$b = \frac{9}{- 4}$

Step 3.2.3.2

Move the negative in front of the fraction.

$b = - \frac{9}{4}$

Step 4

Exclude the solutions that do not make $\sqrt{63 - 7 b - b} = - 9$ true.

$No solution$