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受欢迎的代数 >

solvefor x,(2x-1)(3x+q+2)=3x+q+2

解答

求解

x, (2 x - 1) (3 x + q + 2) = 3 x + q + 2

解答

x = 1, x = - \frac{q + 2}{3}

求解步骤

(2 x - 1) (3 x + q + 2) = 3 x + q + 2

展开

(2 x - 1) (3 x + q + 2) : 6 x^{2} + 2 x q + x - q - 2

6 x^{2} + 2 x q + x - q - 2 = 3 x + q + 2

将

2

para o lado esquerdo

6 x^{2} + 2 x q + x - q - 4 = 3 x + q

将

q

para o lado esquerdo

2 x q - 2 q + 6 x^{2} + x - 4 = 3 x

将

3 x

para o lado esquerdo

6 x^{2} + 2 x q - 2 x - 2 q - 4 = 0

改写成标准形式

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

6 x^{2} + (2 q - 2) x - 2 q - 4 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 2 q - 2 ) \pm ( 2 q - 2 ) ^{2} - 4 \cdot 6 ( - 2 q - 4 )}{2 \cdot 6}

化简

(2 q - 2)^{2} - 4 \cdot 6 (- 2 q - 4) : 2 (q + 5)

x_{1, 2} = \frac{- ( 2 q - 2 ) \pm 2 ( q + 5 )}{2 \cdot 6}

将解分隔开

x_{1} = \frac{- ( 2 q - 2 ) + 2 ( q + 5 )}{2 \cdot 6}, x_{2} = \frac{- ( 2 q - 2 ) - 2 ( q + 5 )}{2 \cdot 6}

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

x = \frac{- ( 2 q - 2 ) - 2 ( q + 5 )}{2 \cdot 6} : - \frac{q + 2}{3}

二次方程组的解是:

x = 1, x = - \frac{q + 2}{3}

作图

流行的例子

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x^{2} + x - 12 = 0, x^{1} = 3 x^{2} = - 4

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