因数 x^2+5x+25/4

解

因数

x^{2} + 5 x + \frac{25}{4}

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

解答ステップ

x^{2} + 5 x + \frac{25}{4}

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

の形式で書き直す

:

\frac{25}{4} = (\frac{5}{2})^{2}

5 x = 2 x \frac{5}{2}

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

完全平方式を適用する:

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

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

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