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受欢迎的代数 >

x^2+(m+4)x+(3m)/2+9/2 =0

解答

x^{2} + (m + 4) x + \frac{3 m}{2} + \frac{9}{2} = 0

解答

x = \frac{- m - 4 + m ^{2} + 2 m - 2}{2}, x = - \frac{m + m ^{2} + 2 m - 2 + 4}{2}

求解步骤

x^{2} + (m + 4) x + \frac{3 m}{2} + \frac{9}{2} = 0

在两边乘以

2

2 x^{2} + 2 x (m + 4) + 3 m + 9 = 0

展开

2 x^{2} + 2 x (m + 4) + 3 m + 9 : 2 x^{2} + 2 m x + 8 x + 3 m + 9

2 x^{2} + 2 m x + 8 x + 3 m + 9 = 0

改写成标准形式

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

2 x^{2} + (2 m + 8) x + 3 m + 9 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 2 m + 8 ) \pm ( 2 m + 8 ) ^{2} - 4 \cdot 2 ( 3 m + 9 )}{2 \cdot 2}

化简

(2 m + 8)^{2} - 4 \cdot 2 (3 m + 9) : 2 m^{2} + 2 m - 2

x_{1, 2} = \frac{- ( 2 m + 8 ) \pm 2 m ^{2} + 2 m - 2}{2 \cdot 2}

将解分隔开

x_{1} = \frac{- ( 2 m + 8 ) + 2 m ^{2} + 2 m - 2}{2 \cdot 2}, x_{2} = \frac{- ( 2 m + 8 ) - 2 m ^{2} + 2 m - 2}{2 \cdot 2}

x = \frac{- ( 2 m + 8 ) + 2 m ^{2} + 2 m - 2}{2 \cdot 2} : \frac{- m - 4 + m ^{2} + 2 m - 2}{2}

x = \frac{- ( 2 m + 8 ) - 2 m ^{2} + 2 m - 2}{2 \cdot 2} : - \frac{m + m ^{2} + 2 m - 2 + 4}{2}

二次方程组的解是:

x = \frac{- m - 4 + m ^{2} + 2 m - 2}{2}, x = - \frac{m + m ^{2} + 2 m - 2 + 4}{2}

作图

流行的例子

solvefor x,x^2+11kx+40=0

so l v e f or x, x^{2} + 11 k x + 40 = 0

(2 x - 3) (x + 6) = 0

5(5x-5)^2-38=-18

5 (5 x - 5)^{2} - 38 = - 18

- 5 x^{2} - 2 x - 8 = 0

w^{2} - 5 w + 4 = 0