What is factor y^2+3y+9/4 ?

The solution to factor y^2+3y+9/4 is (y+3/2)^2

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factor y^2+3y+9/4

factor

y^{2} + 3 y + \frac{9}{4}

(y + \frac{3}{2})^{2}

Solution steps

y^{2} + 3 y + \frac{9}{4}

Rewrite in the form of

a^{2} + 2 ab + b^{2} :

\frac{9}{4} = (\frac{3}{2})^{2}

3 y = 2 y \frac{3}{2}

= y^{2} + 2 y \frac{3}{2} + (\frac{3}{2})^{2}

Apply Perfect Square Formula:

a^{2} + 2 ab + b^{2} = (a + b)^{2}

y^{2} + 2 y \frac{3}{2} + (\frac{3}{2})^{2} = (y + \frac{3}{2})^{2}

= (y + \frac{3}{2})^{2}

m^{2} + m + 2 = 0

(2 x + 4) \cdot (x - 1) + (3 x + 5)^{2} = 3 (2 x + 5)^{2} + x

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