Algebra Examples

$\sqrt{- 3 - k} = 2$

Step 1

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

${\sqrt{- 3 - k}}^{2} = 2^{2}$

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 $\sqrt{- 3 - k}$ as ${(- 3 - k)}^{\frac{1}{2}}$ .

${({(- 3 - k)}^{\frac{1}{2}})}^{2} = 2^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(- 3 - k)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(- 3 - k)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

${(- 3 - k)}^{\frac{1}{2} \cdot 2} = 2^{2}$

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.

${(- 3 - k)}^{\frac{1}{2} \cdot 2} = 2^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(- 3 - k)}^{1} = 2^{2}$

Step 2.2.1.2

Simplify.

$- 3 - k = 2^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

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

$- 3 - k = 4$

Step 3

Solve for $k$ .

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Step 3.1

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

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Step 3.1.1

Add $3$ to both sides of the equation.

$- k = 4 + 3$

Step 3.1.2

Add $4$ and $3$ .

$- k = 7$

Step 3.2

Divide each term in $- k = 7$ by $- 1$ and simplify.

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Step 3.2.1

Divide each term in $- k = 7$ by $- 1$ .

$\frac{- k}{- 1} = \frac{7}{- 1}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Dividing two negative values results in a positive value.

$\frac{k}{1} = \frac{7}{- 1}$

Step 3.2.2.2

Divide $k$ by $1$ .

$k = \frac{7}{- 1}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $7$ by $- 1$ .

$k = - 7$