Algebra Examples

$x + 11 = \frac{1}{18} {(y - 4)}^{2}$

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.

$\frac{1}{18} \cdot {(y - 4)}^{2} = x + 11$

Step 2

Multiply each term in $\frac{1}{18} \cdot {(y - 4)}^{2} = x + 11$ by $18$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{1}{18} \cdot {(y - 4)}^{2} = x + 11$ by $18$ .

$\frac{1}{18} \cdot {(y - 4)}^{2} \cdot 18 = x \cdot 18 + 11 \cdot 18$

Step 2.2

Simplify the left side.

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Step 2.2.1

Combine $\frac{1}{18}$ and ${(y - 4)}^{2}$ .

$\frac{{(y - 4)}^{2}}{18} \cdot 18 = x \cdot 18 + 11 \cdot 18$

Step 2.2.2

Cancel the common factor of $18$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{{(y - 4)}^{2}}{18} \cdot 18 = x \cdot 18 + 11 \cdot 18$

Step 2.2.2.2

Rewrite the expression.

${(y - 4)}^{2} = x \cdot 18 + 11 \cdot 18$

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 $18$ to the left of $x$ .

${(y - 4)}^{2} = 18 \cdot x + 11 \cdot 18$

Step 2.3.1.2

Multiply $11$ by $18$ .

${(y - 4)}^{2} = 18 x + 198$

Step 3

Factor $18$ out of $18 x + 198$ .

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Step 3.1

Factor $18$ out of $18 x$ .

${(y - 4)}^{2} = 18 (x) + 198$

Step 3.2

Factor $18$ out of $198$ .

${(y - 4)}^{2} = 18 x + 18 \cdot 11$

Step 3.3

Factor $18$ out of $18 x + 18 \cdot 11$ .

${(y - 4)}^{2} = 18 (x + 11)$