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受欢迎的代数 >

x 1/4 x-3/5 (x-3)=20

解答

x \frac{1}{4} x - \frac{3}{5} (x - 3) = 20

解答

x = \frac{2 ( 3 + 4 29 )}{5}, x = \frac{2 ( 3 - 4 29 )}{5}

+1

十进制

x = 9.81626 \dots, x = - 7.41626 \dots

求解步骤

x \frac{1}{4} x - \frac{3}{5} (x - 3) = 20

在两边乘以

5

\frac{5}{4} x^{2} - 3 (x - 3) = 100

展开

\frac{5}{4} x^{2} - 3 (x - 3) : \frac{5}{4} x^{2} - 3 x + 9

\frac{5}{4} x^{2} - 3 x + 9 = 100

将

100

para o lado esquerdo

\frac{5}{4} x^{2} - 3 x - 91 = 0

改写成标准形式

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

\frac{5 x ^{2}}{4} - 3 x - 91 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot \frac{5}{4} ( - 91 )}{2 \cdot \frac{5}{4}}

(- 3)^{2} - 4 \cdot \frac{5}{4} (- 91) = 429

x_{1, 2} = \frac{- ( - 3 ) \pm 4 29}{2 \cdot \frac{5}{4}}

将解分隔开

x_{1} = \frac{- ( - 3 ) + 4 29}{2 \cdot \frac{5}{4}}, x_{2} = \frac{- ( - 3 ) - 4 29}{2 \cdot \frac{5}{4}}

x = \frac{- ( - 3 ) + 4 29}{2 \frac{5}{4}} : \frac{2 ( 3 + 4 29 )}{5}

x = \frac{- ( - 3 ) - 4 29}{2 \frac{5}{4}} : \frac{2 ( 3 - 4 29 )}{5}

二次方程组的解是:

x = \frac{2 ( 3 + 4 29 )}{5}, x = \frac{2 ( 3 - 4 29 )}{5}

作图

流行的例子

(d + 3)^{2} = 7

x^{2} - 2 x - \frac{1}{2} = 0

completesquare y^2-16y

co m pl e t es q u a re y^{2} - 16 y

r^{2} = 2

completesquare y^2-24y

co m pl e t es q u a re y^{2} - 24 y