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受欢迎的代数 >

completesquare (5*x)/8+(x^2)/(51)

解答

配方

\frac{5 \cdot x}{8} + \frac{x ^{2}}{51}

解答

\frac{1}{51} (x + \frac{255}{16})^{2} - \frac{1275}{256}

求解步骤

\frac{5 x}{8} + \frac{x ^{2}}{51}

改写成标准形式

a x^{2} + b x + c

\frac{1 \cdot x ^{2}}{51} + \frac{5 x}{8}

将

\frac{1 x ^{2}}{51} + \frac{5 x}{8}

改写为如下形式:

x^{2} + 2 a x + a^{2}

因式分解

\frac{1}{51}

\frac{1}{51} (x^{2} + \frac{255 x}{8})

2 a = \frac{255}{8} : a = \frac{255}{16}

加和减

(\frac{255}{16})^{2}

\frac{1}{51} (x^{2} + \frac{255 x}{8} + (\frac{255}{16})^{2} - (\frac{255}{16})^{2})

x^{2} + 2 a x + a^{2} = (x + a)^{2}

x^{2} + \frac{255}{8} x + (\frac{255}{16})^{2} = (x + \frac{255}{16})^{2}

\frac{1}{51} ((x + \frac{255}{16})^{2} - (\frac{255}{16})^{2})

化简

\frac{1}{51} (x + \frac{255}{16})^{2} - \frac{1275}{256}

作图

流行的例子

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- 160 x^{2} + 450 x - 300 = 0

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1000 x \cdot \frac{x}{2} = 5643 (104 - x)

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