Precalculus Examples

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

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

Step 1

Since

x

$x$ 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

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

Step 2

Add

\frac{26}{5}

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

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

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

Step 3

Divide each term in

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

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

5

$5$ and simplify.

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Step 3.1

Divide each term in

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

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

5

$5$ .

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

$5$ .

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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}

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

Step 3.2.1.2

Divide

{(x + \frac{1}{5})}^{2}

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

1

$1$ .

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

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

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

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

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

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

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}

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

Step 3.3.1.2

Multiply

\frac{26}{5} \cdot \frac{1}{5}

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

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Step 3.3.1.2.1

Multiply

\frac{26}{5}

$\frac{26}{5}$ by

\frac{1}{5}

$\frac{1}{5}$ .

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

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

Step 3.3.1.2.2

Multiply

5

$5$ by

5

$5$ .

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