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受欢迎的代数 >

2x(1+1/2 x)=x(1/2 x+1)+12

解答

2 x (1 + \frac{1}{2} x) = x (\frac{1}{2} x + 1) + 12

解答

x = - 6, x = 4

求解步骤

2 x (1 + \frac{1}{2} x) = x (\frac{1}{2} x + 1) + 12

展开

2 x (1 + \frac{1}{2} x) : 2 x + x^{2}

展开

x (\frac{1}{2} x + 1) + 12 : \frac{1}{2} x^{2} + x + 12

2 x + x^{2} = \frac{1}{2} x^{2} + x + 12

交换两边

\frac{1}{2} x^{2} + x + 12 = 2 x + x^{2}

将

x^{2}

para o lado esquerdo

- \frac{1}{2} x^{2} + x + 12 = 2 x

将

2 x

para o lado esquerdo

- \frac{1}{2} x^{2} - x + 12 = 0

改写成标准形式

a x^{2} + b x + c = 0

- \frac{x ^{2}}{2} - x + 12 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 ( - \frac{1}{2} ) \cdot 12}{2 ( - \frac{1}{2} )}

(- 1)^{2} - 4 (- \frac{1}{2}) \cdot 12 = 5

x_{1, 2} = \frac{- ( - 1 ) \pm 5}{2 ( - \frac{1}{2} )}

将解分隔开

x_{1} = \frac{- ( - 1 ) + 5}{2 ( - \frac{1}{2} )}, x_{2} = \frac{- ( - 1 ) - 5}{2 ( - \frac{1}{2} )}

x = \frac{- ( - 1 ) + 5}{2 ( - \frac{1}{2} )} : - 6

x = \frac{- ( - 1 ) - 5}{2 ( - \frac{1}{2} )} : 4

二次方程组的解是:

x = - 6, x = 4

作图

流行的例子

x^{2} - 1.3 x - 0.3 = 0

32 - 6 x^{2} = 0

c^{2} - 2 c = 6

v^{2} + 3 v - 18 = 10 v

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