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受欢迎的代数 >

(2x-3)(x+c)=ax^2+bx-12

解答

(2 x - 3) (x + c) = a x^{2} + b x - 12

解答

x = \frac{- 2 c + 3 + b + 4 c ^{2} + 12 c - 12 c a - 4 c b + 48 a + b ^{2} + 6 b - 87}{2 ( 2 - a )}, x = \frac{- 2 c + 3 + b - 4 c ^{2} + 12 c - 12 c a - 4 c b + 48 a + b ^{2} + 6 b - 87}{2 ( 2 - a )}; a \neq = 2

求解步骤

(2 x - 3) (x + c) = a x^{2} + b x - 12

展开

(2 x - 3) (x + c) : 2 x^{2} + 2 c x - 3 x - 3 c

2 x^{2} + 2 c x - 3 x - 3 c = a x^{2} + b x - 12

将

12

para o lado esquerdo

2 x^{2} + 2 c x - 3 x - 3 c + 12 = a x^{2} + b x

将

b x

para o lado esquerdo

2 x^{2} + 2 c x - 3 x - 3 c + 12 - b x = a x^{2}

将

a x^{2}

para o lado esquerdo

2 x^{2} + 2 c x - 3 x - 3 c + 12 - b x - a x^{2} = 0

改写成标准形式

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

(2 - a) x^{2} + (2 c - 3 - b) x - 3 c + 12 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 2 c - 3 - b ) \pm ( 2 c - 3 - b ) ^{2} - 4 ( 2 - a ) ( - 3 c + 12 )}{2 ( 2 - a )}

化简

(2 c - 3 - b)^{2} - 4 (2 - a) (- 3 c + 12) : 4 c^{2} + 12 c - 12 c a - 4 c b + 48 a + b^{2} + 6 b - 87

x_{1, 2} = \frac{- ( 2 c - 3 - b ) \pm 4 c ^{2} + 12 c - 12 c a - 4 c b + 48 a + b ^{2} + 6 b - 87}{2 ( 2 - a )}; a \neq = 2

将解分隔开

x_{1} = \frac{- ( 2 c - 3 - b ) + 4 c ^{2} + 12 c - 12 c a - 4 c b + 48 a + b ^{2} + 6 b - 87}{2 ( 2 - a )}, x_{2} = \frac{- ( 2 c - 3 - b ) - 4 c ^{2} + 12 c - 12 c a - 4 c b + 48 a + b ^{2} + 6 b - 87}{2 ( 2 - a )}

x = \frac{- ( 2 c - 3 - b ) + 4 c ^{2} + 12 c - 12 c a - 4 c b + 48 a + b ^{2} + 6 b - 87}{2 ( 2 - a )} : \frac{- 2 c + 3 + b + 4 c ^{2} + 12 c - 12 c a - 4 c b + 48 a + b ^{2} + 6 b - 87}{2 ( 2 - a )}

x = \frac{- ( 2 c - 3 - b ) - 4 c ^{2} + 12 c - 12 c a - 4 c b + 48 a + b ^{2} + 6 b - 87}{2 ( 2 - a )} : \frac{- 2 c + 3 + b - 4 c ^{2} + 12 c - 12 c a - 4 c b + 48 a + b ^{2} + 6 b - 87}{2 ( 2 - a )}

二次方程组的解是:

x = \frac{- 2 c + 3 + b + 4 c ^{2} + 12 c - 12 c a - 4 c b + 48 a + b ^{2} + 6 b - 87}{2 ( 2 - a )}, x = \frac{- 2 c + 3 + b - 4 c ^{2} + 12 c - 12 c a - 4 c b + 48 a + b ^{2} + 6 b - 87}{2 ( 2 - a )}; a \neq = 2

作图

流行的例子

completesquare 3x^2+x-2=0

co m pl e t es q u a re 3 x^{2} + x - 2 = 0

x^{2} = 7 x + 6

(x - 7)^{2} = - 4

(x - 7)^{2} = 22

25z^2-110z+121=16

25 z^{2} - 110 z + 121 = 16