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受欢迎的代数 >

(1/8-x)^2+42=(x+1/8)^2-x/2+x(x-1)

解答

(\frac{1}{8} - x)^{2} + 42 = (x + \frac{1}{8})^{2} - \frac{x}{2} + x (x - 1)

解答

x = - 6, x = 7

求解步骤

(\frac{1}{8} - x)^{2} + 42 = (x + \frac{1}{8})^{2} - \frac{x}{2} + x (x - 1)

在两边乘以

2

2 (\frac{1}{8} - x)^{2} + 84 = 2 (x + \frac{1}{8})^{2} - x + 2 x (x - 1)

展开

2 (\frac{1}{8} - x)^{2} + 84 : \frac{2689}{32} - \frac{1}{2} x + 2 x^{2}

展开

2 (x + \frac{1}{8})^{2} - x + 2 x (x - 1) : 4 x^{2} - \frac{5}{2} x + \frac{1}{32}

\frac{2689}{32} - \frac{1}{2} x + 2 x^{2} = 4 x^{2} - \frac{5}{2} x + \frac{1}{32}

将

\frac{1}{32}

para o lado esquerdo

2 x^{2} - \frac{1}{2} x + 84 = 4 x^{2} - \frac{5}{2} x

将

\frac{5}{2} x

para o lado esquerdo

2 x^{2} + 2 x + 84 = 4 x^{2}

将

4 x^{2}

para o lado esquerdo

- 2 x^{2} + 2 x + 84 = 0

使用求根公式求解

x_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 ( - 2 ) \cdot 84}{2 ( - 2 )}

2^{2} - 4 (- 2) \cdot 84 = 26

x_{1, 2} = \frac{- 2 \pm 26}{2 ( - 2 )}

将解分隔开

x_{1} = \frac{- 2 + 26}{2 ( - 2 )}, x_{2} = \frac{- 2 - 26}{2 ( - 2 )}

x = \frac{- 2 + 26}{2 ( - 2 )} : - 6

x = \frac{- 2 - 26}{2 ( - 2 )} : 7

二次方程组的解是:

x = - 6, x = 7

作图

流行的例子

2 q^{2} - 3 q - 15 = - 4 q

11d^2-12d+4=6d^2

11 d^{2} - 12 d + 4 = 6 d^{2}

- x^{2} = 8 x - 2

9 q^{2} + 30 q + 25 = 0

completesquare 1+4x-x^2

co m pl e t es q u a re 1 + 4 x - x^{2}