Precalculus Examples

${(x + 10)}^{2} = 4 (\frac{26}{125}) (y + 210)$

Step 1

Rewrite the equation as $4 (\frac{26}{125}) \cdot (y + 210) = {(x + 10)}^{2}$ .

$4 (\frac{26}{125}) \cdot (y + 210) = {(x + 10)}^{2}$

Step 2

Multiply $4 (\frac{26}{125})$ .

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Step 2.1

Combine $4$ and $\frac{26}{125}$ .

$\frac{4 \cdot 26}{125} \cdot (y + 210) = {(x + 10)}^{2}$

Step 2.2

Multiply $4$ by $26$ .

$\frac{104}{125} \cdot (y + 210) = {(x + 10)}^{2}$

Step 3

Multiply each term in $\frac{104}{125} \cdot (y + 210) = {(x + 10)}^{2}$ by $\frac{125}{104}$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{104}{125} \cdot (y + 210) = {(x + 10)}^{2}$ by $\frac{125}{104}$ .

$\frac{104}{125} \cdot (y + 210) \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Apply the distributive property.

$(\frac{104}{125} y + \frac{104}{125} \cdot 210) \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.2

Combine $\frac{104}{125}$ and $y$ .

$(\frac{104 y}{125} + \frac{104}{125} \cdot 210) \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.3

Cancel the common factor of $5$ .

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Step 3.2.3.1

Factor $5$ out of $125$ .

$(\frac{104 y}{125} + \frac{104}{5 (25)} \cdot 210) \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.3.2

Factor $5$ out of $210$ .

$(\frac{104 y}{125} + \frac{104}{5 \cdot 25} \cdot (5 \cdot 42)) \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.3.3

Cancel the common factor.

$(\frac{104 y}{125} + \frac{104}{5 \cdot 25} \cdot (5 \cdot 42)) \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.3.4

Rewrite the expression.

$(\frac{104 y}{125} + \frac{104}{25} \cdot 42) \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.4

Combine $\frac{104}{25}$ and $42$ .

$(\frac{104 y}{125} + \frac{104 \cdot 42}{25}) \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.5

Multiply $104$ by $42$ .

$(\frac{104 y}{125} + \frac{4368}{25}) \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.6

Apply the distributive property.

$\frac{104 y}{125} \cdot \frac{125}{104} + \frac{4368}{25} \cdot \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.7

Cancel the common factor of $104$ .

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Step 3.2.7.1

Factor $104$ out of $104 y$ .

$\frac{104 (y)}{125} \cdot \frac{125}{104} + \frac{4368}{25} \cdot \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.7.2

Cancel the common factor.

$\frac{104 y}{125} \cdot \frac{125}{104} + \frac{4368}{25} \cdot \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.7.3

Rewrite the expression.

$\frac{y}{125} \cdot 125 + \frac{4368}{25} \cdot \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.8

Cancel the common factor of $125$ .

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Step 3.2.8.1

Cancel the common factor.

$\frac{y}{125} \cdot 125 + \frac{4368}{25} \cdot \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.8.2

Rewrite the expression.

$y + \frac{4368}{25} \cdot \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.9

Cancel the common factor of $104$ .

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Step 3.2.9.1

Factor $104$ out of $4368$ .

$y + \frac{104 (42)}{25} \cdot \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.9.2

Cancel the common factor.

$y + \frac{104 \cdot 42}{25} \cdot \frac{125}{104} = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.9.3

Rewrite the expression.

$y + \frac{42}{25} \cdot 125 = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.10

Cancel the common factor of $25$ .

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Step 3.2.10.1

Factor $25$ out of $125$ .

$y + \frac{42}{25} \cdot (25 (5)) = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.10.2

Cancel the common factor.

$y + \frac{42}{25} \cdot (25 \cdot 5) = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.10.3

Rewrite the expression.

$y + 42 \cdot 5 = {(x + 10)}^{2} \frac{125}{104}$

Step 3.2.11

Multiply $42$ by $5$ .

$y + 210 = {(x + 10)}^{2} \frac{125}{104}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Combine ${(x + 10)}^{2}$ and $\frac{125}{104}$ .

$y + 210 = \frac{{(x + 10)}^{2} \cdot 125}{104}$

Step 3.3.2

Move $125$ to the left of ${(x + 10)}^{2}$ .

$y + 210 = \frac{125 {(x + 10)}^{2}}{104}$

Step 4

Subtract $210$ from both sides of the equation.

$y = \frac{125 {(x + 10)}^{2}}{104} - 210$