Precalculus Examples

$x = - \frac{1}{8} {(y + 3)}^{2} - 2$

Step 1

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

$- \frac{1}{8} \cdot {(y + 3)}^{2} - 2 = x$

Step 2

Add $2$ to both sides of the equation.

$- \frac{1}{8} \cdot {(y + 3)}^{2} = x + 2$

Step 3

Multiply each term in $- \frac{1}{8} \cdot {(y + 3)}^{2} = x + 2$ by $- 8$ to eliminate the fractions.

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Step 3.1

Multiply each term in $- \frac{1}{8} \cdot {(y + 3)}^{2} = x + 2$ by $- 8$ .

$- \frac{1}{8} \cdot {(y + 3)}^{2} \cdot - 8 = x \cdot - 8 + 2 \cdot - 8$

Step 3.2

Simplify the left side.

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Step 3.2.1

Combine ${(y + 3)}^{2}$ and $\frac{1}{8}$ .

$- \frac{{(y + 3)}^{2}}{8} \cdot - 8 = x \cdot - 8 + 2 \cdot - 8$

Step 3.2.2

Cancel the common factor of $8$ .

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Step 3.2.2.1

Move the leading negative in $- \frac{{(y + 3)}^{2}}{8}$ into the numerator.

$\frac{- {(y + 3)}^{2}}{8} \cdot - 8 = x \cdot - 8 + 2 \cdot - 8$

Step 3.2.2.2

Factor $8$ out of $- 8$ .

$\frac{- {(y + 3)}^{2}}{8} \cdot (8 (- 1)) = x \cdot - 8 + 2 \cdot - 8$

Step 3.2.2.3

Cancel the common factor.

$\frac{- {(y + 3)}^{2}}{8} \cdot (8 \cdot - 1) = x \cdot - 8 + 2 \cdot - 8$

Step 3.2.2.4

Rewrite the expression.

$- {(y + 3)}^{2} \cdot - 1 = x \cdot - 8 + 2 \cdot - 8$

Step 3.2.3

Multiply.

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Step 3.2.3.1

Multiply $- 1$ by $- 1$ .

$1 {(y + 3)}^{2} = x \cdot - 8 + 2 \cdot - 8$

Step 3.2.3.2

Multiply ${(y + 3)}^{2}$ by $1$ .

${(y + 3)}^{2} = x \cdot - 8 + 2 \cdot - 8$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Move $- 8$ to the left of $x$ .

${(y + 3)}^{2} = - 8 \cdot x + 2 \cdot - 8$

Step 3.3.1.2

Multiply $2$ by $- 8$ .

${(y + 3)}^{2} = - 8 x - 16$

Step 4

Factor.

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Step 4.1

Factor $8$ out of $- 8 x - 16$ .

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Step 4.1.1

Factor $8$ out of $- 8 x$ .

${(y + 3)}^{2} = 8 (- x) - 16$

Step 4.1.2

Factor $8$ out of $- 16$ .

${(y + 3)}^{2} = 8 (- x) + 8 (- 2)$

Step 4.1.3

Factor $8$ out of $8 (- x) + 8 (- 2)$ .

${(y + 3)}^{2} = 8 (- x - 2)$

Step 4.2

Factor $- 1$ out of $- x$ .

${(y + 3)}^{2} = 8 (- (x) - 2)$

Step 4.3

Rewrite $- 2$ as $- 1 (2)$ .

${(y + 3)}^{2} = 8 (- (x) - 1 (2))$

Step 4.4

Factor $- 1$ out of $- (x) - 1 (2)$ .

${(y + 3)}^{2} = 8 (- (x + 2))$

Step 4.5

Multiply $- 1$ by $8$ .

${(y + 3)}^{2} = - 8 (x + 2)$