Precalculus Examples

$y - 5 = - 2 {(x + 1)}^{2}$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 2 {(x + 1)}^{2} = y - 5$

Step 2

Divide each term in $- 2 {(x + 1)}^{2} = y - 5$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 {(x + 1)}^{2} = y - 5$ by $- 2$ .

$\frac{- 2 {(x + 1)}^{2}}{- 2} = \frac{y}{- 2} + \frac{- 5}{- 2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 2 {(x + 1)}^{2}}{- 2} = \frac{y}{- 2} + \frac{- 5}{- 2}$

Step 2.2.1.2

Divide ${(x + 1)}^{2}$ by $1$ .

${(x + 1)}^{2} = \frac{y}{- 2} + \frac{- 5}{- 2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Move the negative in front of the fraction.

${(x + 1)}^{2} = - \frac{y}{2} + \frac{- 5}{- 2}$

Step 2.3.1.2

Dividing two negative values results in a positive value.

${(x + 1)}^{2} = - \frac{y}{2} + \frac{5}{2}$

Step 3

Factor.

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Step 3.1

Combine the numerators over the common denominator.

${(x + 1)}^{2} = \frac{- y + 5}{2}$

Step 3.2

Factor $- 1$ out of $- y$ .

${(x + 1)}^{2} = \frac{- (y) + 5}{2}$

Step 3.3

Rewrite $5$ as $- 1 (- 5)$ .

${(x + 1)}^{2} = \frac{- (y) - 1 (- 5)}{2}$

Step 3.4

Factor $- 1$ out of $- (y) - 1 (- 5)$ .

${(x + 1)}^{2} = \frac{- (y - 5)}{2}$

Step 3.5

Move the negative in front of the fraction.

${(x + 1)}^{2} = - \frac{y - 5}{2}$

Step 3.6

Reorder terms.

${(x + 1)}^{2} = - (\frac{1}{2} (y - 5))$

Step 3.7

Remove parentheses.

${(x + 1)}^{2} = - \frac{1}{2} (y - 5)$