Examples

$y = 5 {(x + \frac{1}{5})}^{2} - \frac{26}{5}$

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.

$5 {(x + \frac{1}{5})}^{2} - \frac{26}{5} = y$

Step 2

Add $\frac{26}{5}$ to both sides of the equation.

$5 {(x + \frac{1}{5})}^{2} = y + \frac{26}{5}$

Step 3

Divide each term in $5 {(x + \frac{1}{5})}^{2} = y + \frac{26}{5}$ by $5$ and simplify.

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Step 3.1

Divide each term in $5 {(x + \frac{1}{5})}^{2} = y + \frac{26}{5}$ by $5$ .

$\frac{5 {(x + \frac{1}{5})}^{2}}{5} = \frac{y}{5} + \frac{\frac{26}{5}}{5}$

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.

$\frac{5 {(x + \frac{1}{5})}^{2}}{5} = \frac{y}{5} + \frac{\frac{26}{5}}{5}$

Step 3.2.1.2

Divide ${(x + \frac{1}{5})}^{2}$ by $1$ .

${(x + \frac{1}{5})}^{2} = \frac{y}{5} + \frac{\frac{26}{5}}{5}$

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

Multiply the numerator by the reciprocal of the denominator.

${(x + \frac{1}{5})}^{2} = \frac{y}{5} + \frac{26}{5} \cdot \frac{1}{5}$

Step 3.3.1.2

Multiply $\frac{26}{5} \cdot \frac{1}{5}$ .

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Step 3.3.1.2.1

Multiply $\frac{26}{5}$ by $\frac{1}{5}$ .

${(x + \frac{1}{5})}^{2} = \frac{y}{5} + \frac{26}{5 \cdot 5}$

Step 3.3.1.2.2

Multiply $5$ by $5$ .

${(x + \frac{1}{5})}^{2} = \frac{y}{5} + \frac{26}{25}$

Step 4

Factor.

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Step 4.1

To write $\frac{y}{5}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

${(x + \frac{1}{5})}^{2} = \frac{y}{5} \cdot \frac{5}{5} + \frac{26}{25}$

Step 4.2

Write each expression with a common denominator of $25$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.2.1

Multiply $\frac{y}{5}$ by $\frac{5}{5}$ .

${(x + \frac{1}{5})}^{2} = \frac{y \cdot 5}{5 \cdot 5} + \frac{26}{25}$

Step 4.2.2

Multiply $5$ by $5$ .

${(x + \frac{1}{5})}^{2} = \frac{y \cdot 5}{25} + \frac{26}{25}$

Step 4.3

Combine the numerators over the common denominator.

${(x + \frac{1}{5})}^{2} = \frac{y \cdot 5 + 26}{25}$

Step 4.4

Move $5$ to the left of $y$ .

${(x + \frac{1}{5})}^{2} = \frac{5 y + 26}{25}$

Step 4.5

Reorder terms.

${(x + \frac{1}{5})}^{2} = \frac{1}{25} (5 y + 26)$

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