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受欢迎的代数 >

2x^2-3x+21=a(x-b)^2+c

解答

2 x^{2} - 3 x + 21 = a (x - b)^{2} + c

解答

x = \frac{3 - 2 ab + 8 a b ^{2} + 84 a - 12 ab - 4 a c + 8 c - 159}{2 ( 2 - a )}, x = \frac{3 - 2 ab - 8 a b ^{2} + 84 a - 12 ab - 4 a c + 8 c - 159}{2 ( 2 - a )}; a \neq = 2

求解步骤

2 x^{2} - 3 x + 21 = a (x - b)^{2} + c

展开

a (x - b)^{2} + c : a x^{2} - 2 ab x + a b^{2} + c

2 x^{2} - 3 x + 21 = a x^{2} - 2 ab x + a b^{2} + c

将

c

para o lado esquerdo

2 x^{2} - 3 x + 21 - c = a x^{2} - 2 ab x + a b^{2}

将

a b^{2}

para o lado esquerdo

2 x^{2} - 3 x + 21 - c - a b^{2} = a x^{2} - 2 ab x

将

2 ab x

para o lado esquerdo

2 x^{2} - 3 x + 21 - c - a b^{2} + 2 ab x = a x^{2}

将

a x^{2}

para o lado esquerdo

2 x^{2} - 3 x + 21 - c - a b^{2} + 2 ab x - a x^{2} = 0

改写成标准形式

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

(2 - a) x^{2} + (- 3 + 2 ab) x + 21 - c - a b^{2} = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 3 + 2 ab ) \pm ( - 3 + 2 ab ) ^{2} - 4 ( 2 - a ) ( 21 - c - a b ^{2} )}{2 ( 2 - a )}

化简

(- 3 + 2 ab)^{2} - 4 (2 - a) (21 - c - a b^{2}) : 8 a b^{2} + 84 a - 12 ab - 4 a c + 8 c - 159

x_{1, 2} = \frac{- ( - 3 + 2 ab ) \pm 8 a b ^{2} + 84 a - 12 ab - 4 a c + 8 c - 159}{2 ( 2 - a )}; a \neq = 2

将解分隔开

x_{1} = \frac{- ( - 3 + 2 ab ) + 8 a b ^{2} + 84 a - 12 ab - 4 a c + 8 c - 159}{2 ( 2 - a )}, x_{2} = \frac{- ( - 3 + 2 ab ) - 8 a b ^{2} + 84 a - 12 ab - 4 a c + 8 c - 159}{2 ( 2 - a )}

x = \frac{- ( - 3 + 2 ab ) + 8 a b ^{2} + 84 a - 12 ab - 4 a c + 8 c - 159}{2 ( 2 - a )} : \frac{3 - 2 ab + 8 a b ^{2} + 84 a - 12 ab - 4 a c + 8 c - 159}{2 ( 2 - a )}

x = \frac{- ( - 3 + 2 ab ) - 8 a b ^{2} + 84 a - 12 ab - 4 a c + 8 c - 159}{2 ( 2 - a )} : \frac{3 - 2 ab - 8 a b ^{2} + 84 a - 12 ab - 4 a c + 8 c - 159}{2 ( 2 - a )}

二次方程组的解是:

x = \frac{3 - 2 ab + 8 a b ^{2} + 84 a - 12 ab - 4 a c + 8 c - 159}{2 ( 2 - a )}, x = \frac{3 - 2 ab - 8 a b ^{2} + 84 a - 12 ab - 4 a c + 8 c - 159}{2 ( 2 - a )}; a \neq = 2

作图

流行的例子

0.000015(x+100)^2=0.225375

0.000015 (x + 100)^{2} = 0.225375

5 y + 2 y^{2} = 12

solvefor x,f(x+3)=4x^2+4x-3

so l v e f or x, f (x + 3) = 4 x^{2} + 4 x - 3

x^2+2x-48=(x+8)

x^{2} + 2 x - 48 = (x + 8)

0 = 30 - 4.9 x^{2}