Basic Math Examples

$\sqrt{6 - b} = 2 b \sqrt{6 - b}$

Step 1

Solve for $\sqrt{6 - b}$ .

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Step 1.1

Subtract $2 b \sqrt{6 - b}$ from both sides of the equation.

$\sqrt{6 - b} - 2 b \sqrt{6 - b} = 0$

Step 1.2

Factor $\sqrt{6 - b}$ out of $\sqrt{6 - b} - 2 b \sqrt{6 - b}$ .

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Step 1.2.1

Factor $\sqrt{6 - b}$ out of ${\sqrt{6 - b}}^{1}$ .

$\sqrt{6 - b} \cdot 1 - 2 b \sqrt{6 - b} = 0$

Step 1.2.2

Factor $\sqrt{6 - b}$ out of $- 2 b \sqrt{6 - b}$ .

$\sqrt{6 - b} \cdot 1 + \sqrt{6 - b} (- 2 b) = 0$

Step 1.2.3

Factor $\sqrt{6 - b}$ out of $\sqrt{6 - b} \cdot 1 + \sqrt{6 - b} (- 2 b)$ .

$\sqrt{6 - b} (1 - 2 b) = 0$

Step 1.3

Divide each term in $\sqrt{6 - b} (1 - 2 b) = 0$ by $1 - 2 b$ and simplify.

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Step 1.3.1

Divide each term in $\sqrt{6 - b} (1 - 2 b) = 0$ by $1 - 2 b$ .

$\frac{\sqrt{6 - b} (1 - 2 b)}{1 - 2 b} = \frac{0}{1 - 2 b}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $1 - 2 b$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{\sqrt{6 - b} (1 - 2 b)}{1 - 2 b} = \frac{0}{1 - 2 b}$

Step 1.3.2.1.2

Divide $\sqrt{6 - b}$ by $1$ .

$\sqrt{6 - b} = \frac{0}{1 - 2 b}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Divide $0$ by $1 - 2 b$ .

$\sqrt{6 - b} = 0$

Step 2

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

${\sqrt{6 - b}}^{2} = 0^{2}$

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 $\sqrt{6 - b}$ as ${(6 - b)}^{\frac{1}{2}}$ .

${({(6 - b)}^{\frac{1}{2}})}^{2} = 0^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(6 - b)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(6 - b)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(6 - b)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(6 - b)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(6 - b)}^{1} = 0^{2}$

Step 3.2.1.2

Simplify.

$6 - b = 0^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raising $0$ to any positive power yields $0$ .

$6 - b = 0$

Step 4

Solve for $b$ .

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Step 4.1

Subtract $6$ from both sides of the equation.

$- b = - 6$

Step 4.2

Divide each term in $- b = - 6$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- b = - 6$ by $- 1$ .

$\frac{- b}{- 1} = \frac{- 6}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{b}{1} = \frac{- 6}{- 1}$

Step 4.2.2.2

Divide $b$ by $1$ .

$b = \frac{- 6}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 6$ by $- 1$ .

$b = 6$