Precalculus Examples

$- \sqrt{11 - 2 u} = 15$

Step 1

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

${(- \sqrt{11 - 2 u})}^{2} = 15^{2}$

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 $\sqrt{11 - 2 u}$ as ${(11 - 2 u)}^{\frac{1}{2}}$ .

${(- {(11 - 2 u)}^{\frac{1}{2}})}^{2} = 15^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${(- {(11 - 2 u)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

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

${(- 1)}^{2} {({(11 - 2 u)}^{\frac{1}{2}})}^{2} = 15^{2}$

Step 2.2.1.2

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

$1 {({(11 - 2 u)}^{\frac{1}{2}})}^{2} = 15^{2}$

Step 2.2.1.3

Multiply ${({(11 - 2 u)}^{\frac{1}{2}})}^{2}$ by $1$ .

${({(11 - 2 u)}^{\frac{1}{2}})}^{2} = 15^{2}$

Step 2.2.1.4

Multiply the exponents in ${({(11 - 2 u)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.4.1

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

${(11 - 2 u)}^{\frac{1}{2} \cdot 2} = 15^{2}$

Step 2.2.1.4.2

Cancel the common factor of $2$ .

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Step 2.2.1.4.2.1

Cancel the common factor.

${(11 - 2 u)}^{\frac{1}{2} \cdot 2} = 15^{2}$

Step 2.2.1.4.2.2

Rewrite the expression.

${(11 - 2 u)}^{1} = 15^{2}$

Step 2.2.1.5

Simplify.

$11 - 2 u = 15^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $15$ to the power of $2$ .

$11 - 2 u = 225$

Step 3

Solve for $u$ .

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Step 3.1

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

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Step 3.1.1

Subtract $11$ from both sides of the equation.

$- 2 u = 225 - 11$

Step 3.1.2

Subtract $11$ from $225$ .

$- 2 u = 214$

Step 3.2

Divide each term in $- 2 u = 214$ by $- 2$ and simplify.

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Step 3.2.1

Divide each term in $- 2 u = 214$ by $- 2$ .

$\frac{- 2 u}{- 2} = \frac{214}{- 2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 2 u}{- 2} = \frac{214}{- 2}$

Step 3.2.2.1.2

Divide $u$ by $1$ .

$u = \frac{214}{- 2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $214$ by $- 2$ .

$u = - 107$

Step 4

Exclude the solutions that do not make $- \sqrt{11 - 2 u} = 15$ true.

$No solution$