Algebra Examples

$y = - 5 {(x - 3)}^{2} - 9$

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.

$- 5 {(x - 3)}^{2} - 9 = y$

Step 2

Add $9$ to both sides of the equation.

$- 5 {(x - 3)}^{2} = y + 9$

Step 3

Divide each term in $- 5 {(x - 3)}^{2} = y + 9$ by $- 5$ and simplify.

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Step 3.1

Divide each term in $- 5 {(x - 3)}^{2} = y + 9$ by $- 5$ .

$\frac{- 5 {(x - 3)}^{2}}{- 5} = \frac{y}{- 5} + \frac{9}{- 5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 5 {(x - 3)}^{2}}{- 5} = \frac{y}{- 5} + \frac{9}{- 5}$

Step 3.2.1.2

Divide ${(x - 3)}^{2}$ by $1$ .

${(x - 3)}^{2} = \frac{y}{- 5} + \frac{9}{- 5}$

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 the negative in front of the fraction.

${(x - 3)}^{2} = - \frac{y}{5} + \frac{9}{- 5}$

Step 3.3.1.2

Move the negative in front of the fraction.

${(x - 3)}^{2} = - \frac{y}{5} - \frac{9}{5}$

Step 4

Factor.

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Step 4.1

Factor $- 1$ out of $- \frac{y}{5} - \frac{9}{5}$ .

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Step 4.1.1

Factor $- 1$ out of $- \frac{y}{5}$ .

${(x - 3)}^{2} = - (\frac{y}{5}) - \frac{9}{5}$

Step 4.1.2

Factor $- 1$ out of $- \frac{9}{5}$ .

${(x - 3)}^{2} = - (\frac{y}{5}) - (\frac{9}{5})$

Step 4.1.3

Factor $- 1$ out of $- (\frac{y}{5}) - (\frac{9}{5})$ .

${(x - 3)}^{2} = - (\frac{y}{5} + \frac{9}{5})$

Step 4.2

Combine the numerators over the common denominator.

${(x - 3)}^{2} = - \frac{y + 9}{5}$

Step 4.3

Reorder terms.

${(x - 3)}^{2} = - (\frac{1}{5} (y + 9))$

Step 4.4

Remove parentheses.

${(x - 3)}^{2} = - \frac{1}{5} (y + 9)$