Finite Math Examples

$y = \sqrt{17 - x}$

Step 1

Rewrite the equation as $\sqrt{17 - x} = y$ .

$\sqrt{17 - x} = y$

Step 2

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

${\sqrt{17 - x}}^{2} = y^{2}$

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 $\sqrt{17 - x}$ as ${(17 - x)}^{\frac{1}{2}}$ .

${({(17 - x)}^{\frac{1}{2}})}^{2} = y^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(17 - x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(17 - x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(17 - x)}^{\frac{1}{2} \cdot 2} = y^{2}$

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.

${(17 - x)}^{\frac{1}{2} \cdot 2} = y^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(17 - x)}^{1} = y^{2}$

Step 3.2.1.2

Simplify.

$17 - x = y^{2}$

Step 4

Solve for $x$ .

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Step 4.1

Subtract $17$ from both sides of the equation.

$- x = y^{2} - 17$

Step 4.2

Divide each term in $- x = y^{2} - 17$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- x = y^{2} - 17$ by $- 1$ .

$\frac{- x}{- 1} = \frac{y^{2}}{- 1} + \frac{- 17}{- 1}$

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.

$\frac{x}{1} = \frac{y^{2}}{- 1} + \frac{- 17}{- 1}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{y^{2}}{- 1} + \frac{- 17}{- 1}$

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 $\frac{y^{2}}{- 1}$ .

$x = - 1 \cdot y^{2} + \frac{- 17}{- 1}$

Step 4.2.3.1.2

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

$x = - y^{2} + \frac{- 17}{- 1}$

Step 4.2.3.1.3

Divide $- 17$ by $- 1$ .

$x = - y^{2} + 17$