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受欢迎的代数 >

2x^2=(6/7)x+2

解答

2 x^{2} = (\frac{6}{7}) x + 2

解答

x = \frac{3 + 205}{14}, x = \frac{3 - 205}{14}

+1

十进制

x = 1.23698 \dots, x = - 0.80841 \dots

求解步骤

2 x^{2} = (\frac{6}{7}) x + 2

整理后得

2 x^{2} = \frac{6}{7} x + 2

将

2

para o lado esquerdo

2 x^{2} - 2 = \frac{6}{7} x

将

\frac{6}{7} x

para o lado esquerdo

2 x^{2} - 2 - \frac{6}{7} x = 0

改写成标准形式

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

2 x^{2} - \frac{6 x}{7} - 2 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - \frac{6}{7} ) \pm ( - \frac{6}{7} ) ^{2} - 4 \cdot 2 ( - 2 )}{2 \cdot 2}

(- \frac{6}{7})^{2} - 4 \cdot 2 (- 2) = \frac{2 205}{7}

x_{1, 2} = \frac{- ( - \frac{6}{7} ) \pm \frac{2 205}{7}}{2 \cdot 2}

将解分隔开

x_{1} = \frac{- ( - \frac{6}{7} ) + \frac{2 205}{7}}{2 \cdot 2}, x_{2} = \frac{- ( - \frac{6}{7} ) - \frac{2 205}{7}}{2 \cdot 2}

x = \frac{- ( - \frac{6}{7} ) + \frac{2 205}{7}}{2 \cdot 2} : \frac{3 + 205}{14}

x = \frac{- ( - \frac{6}{7} ) - \frac{2 205}{7}}{2 \cdot 2} : \frac{3 - 205}{14}

二次方程组的解是:

x = \frac{3 + 205}{14}, x = \frac{3 - 205}{14}

作图

流行的例子

completesquare x^2+8x=-15

co m pl e t es q u a re x^{2} + 8 x = - 15

(y + 1)^{2} = 0

m^{2} - 15 m + 54 = 0

t^{2} - 2 t = 63

solvefor x,9x^2-54x+9y^2+6y+91=0

so l v e f or x, 9 x^{2} - 54 x + 9 y^{2} + 6 y + 91 = 0