Basic Math Examples

$0 = 11 - \sqrt{12 + 11 w}$

Step 1

Rewrite the equation as $11 - \sqrt{12 + 11 w} = 0$ .

$11 - \sqrt{12 + 11 w} = 0$

Step 2

Subtract $11$ from both sides of the equation.

$- \sqrt{12 + 11 w} = - 11$

Step 3

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

${(- \sqrt{12 + 11 w})}^{2} = {(- 11)}^{2}$

Step 4

Simplify each side of the equation.

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{12 + 11 w}$ as ${(12 + 11 w)}^{\frac{1}{2}}$ .

${(- {(12 + 11 w)}^{\frac{1}{2}})}^{2} = {(- 11)}^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify ${(- {(12 + 11 w)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1

Apply the product rule to $- {(12 + 11 w)}^{\frac{1}{2}}$ .

${(- 1)}^{2} {({(12 + 11 w)}^{\frac{1}{2}})}^{2} = {(- 11)}^{2}$

Step 4.2.1.2

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

$1 {({(12 + 11 w)}^{\frac{1}{2}})}^{2} = {(- 11)}^{2}$

Step 4.2.1.3

Multiply ${({(12 + 11 w)}^{\frac{1}{2}})}^{2}$ by $1$ .

${({(12 + 11 w)}^{\frac{1}{2}})}^{2} = {(- 11)}^{2}$

Step 4.2.1.4

Multiply the exponents in ${({(12 + 11 w)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.4.1

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

${(12 + 11 w)}^{\frac{1}{2} \cdot 2} = {(- 11)}^{2}$

Step 4.2.1.4.2

Cancel the common factor of $2$ .

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Step 4.2.1.4.2.1

Cancel the common factor.

${(12 + 11 w)}^{\frac{1}{2} \cdot 2} = {(- 11)}^{2}$

Step 4.2.1.4.2.2

Rewrite the expression.

${(12 + 11 w)}^{1} = {(- 11)}^{2}$

Step 4.2.1.5

Simplify.

$12 + 11 w = {(- 11)}^{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Raise $- 11$ to the power of $2$ .

$12 + 11 w = 121$

Step 5

Solve for $w$ .

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Step 5.1

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

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Step 5.1.1

Subtract $12$ from both sides of the equation.

$11 w = 121 - 12$

Step 5.1.2

Subtract $12$ from $121$ .

$11 w = 109$

Step 5.2

Divide each term in $11 w = 109$ by $11$ and simplify.

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Step 5.2.1

Divide each term in $11 w = 109$ by $11$ .

$\frac{11 w}{11} = \frac{109}{11}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $11$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{11 w}{11} = \frac{109}{11}$

Step 5.2.2.1.2

Divide $w$ by $1$ .

$w = \frac{109}{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$w = \frac{109}{11}$

Decimal Form:

$w = 9.\overline{90}$

Mixed Number Form:

$w = 9 \frac{10}{11}$