Algebra Examples

$y^{2} + 25 y + 200$

Step 1

To find the $c$ value $c = {(\frac{b}{2})}^{2}$ , divide the coefficient of $y$ by $2$ and square the result.

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Step 1.1

Apply the product rule to $\frac{25}{2}$ .

$\frac{25^{2}}{2^{2}}$

Step 1.2

Raise $25$ to the power of $2$ .

$\frac{625}{2^{2}}$

Step 1.3

Raise $2$ to the power of $2$ .

$\frac{625}{4}$

Step 2

Add $\frac{625}{4}$ to get the perfect square trinomial.

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Step 2.1

To write $200$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y^{2} + 25 y + 200 \cdot \frac{4}{4} + \frac{625}{4}$

Step 2.2

Combine $200$ and $\frac{4}{4}$ .

$y^{2} + 25 y + \frac{200 \cdot 4}{4} + \frac{625}{4}$

Step 2.3

Combine the numerators over the common denominator.

$y^{2} + 25 y + \frac{200 \cdot 4 + 625}{4}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $200$ by $4$ .

$y^{2} + 25 y + \frac{800 + 625}{4}$

Step 2.4.2

Add $800$ and $625$ .

$y^{2} + 25 y + \frac{1425}{4}$