What is factor x^2+7x+49/4 ?

The solution to factor x^2+7x+49/4 is (x+7/2)^2

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factor x^2+7x+49/4

factor

x^{2} + 7 x + \frac{49}{4}

(x + \frac{7}{2})^{2}

Solution steps

x^{2} + 7 x + \frac{49}{4}

Rewrite in the form of

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

\frac{49}{4} = (\frac{7}{2})^{2}

7 x = 2 x \frac{7}{2}

= x^{2} + 2 x \frac{7}{2} + (\frac{7}{2})^{2}

Apply Perfect Square Formula:

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

x^{2} + 2 x \frac{7}{2} + (\frac{7}{2})^{2} = (x + \frac{7}{2})^{2}

= (x + \frac{7}{2})^{2}

900

2 x (x - 2) + 6 = 2 (x^{2} + 2)

x - 11 = - 5 x^{2}

49 x^{2} + 16 = 56 x

(y^{3} - 7 x^{4} y^{4}) + (- 10 x^{4} y^{3} + 6 y^{3} + 4 x^{4} y^{4}) - (x^{4} y^{3} + 6 x^{4} y^{4})