Algebra Examples

$y = \sqrt{2 m - k}$

Step 1

Rewrite the equation as $\sqrt{2 m - k} = y$ .

$\sqrt{2 m - k} = y$

Step 2

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

${\sqrt{2 m - k}}^{2} = y^{2}$

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

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

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Step 3.2.1.1.1

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

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

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.

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

Step 3.2.1.1.2.2

Rewrite the expression.

${(2 m - k)}^{1} = y^{2}$

Step 3.2.1.2

Simplify.

$2 m - k = y^{2}$

Step 4

Solve for $k$ .

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Step 4.1

Subtract $2 m$ from both sides of the equation.

$- k = y^{2} - 2 m$

Step 4.2

Divide each term in $- k = y^{2} - 2 m$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- k = y^{2} - 2 m$ by $- 1$ .

$\frac{- k}{- 1} = \frac{y^{2}}{- 1} + \frac{- 2 m}{- 1}$

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.

$\frac{k}{1} = \frac{y^{2}}{- 1} + \frac{- 2 m}{- 1}$

Step 4.2.2.2

Divide $k$ by $1$ .

$k = \frac{y^{2}}{- 1} + \frac{- 2 m}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Simplify each term.

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Step 4.2.3.1.1

Move the negative one from the denominator of $\frac{y^{2}}{- 1}$ .

$k = - 1 \cdot y^{2} + \frac{- 2 m}{- 1}$

Step 4.2.3.1.2

Rewrite $- 1 \cdot y^{2}$ as $- y^{2}$ .

$k = - y^{2} + \frac{- 2 m}{- 1}$

Step 4.2.3.1.3

Move the negative one from the denominator of $\frac{- 2 m}{- 1}$ .

$k = - y^{2} - 1 \cdot (- 2 m)$

Step 4.2.3.1.4

Rewrite $- 1 \cdot (- 2 m)$ as $- (- 2 m)$ .

$k = - y^{2} - (- 2 m)$

Step 4.2.3.1.5

Multiply $- 2$ by $- 1$ .

$k = - y^{2} + 2 m$