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受欢迎的代数 >

4(5x+1)^2=x-2020

解答

4 (5 x + 1)^{2} = x - 2020

解答

x = - \frac{39}{200} + i \frac{808079}{200}, x = - \frac{39}{200} - i \frac{808079}{200}

求解步骤

4 (5 x + 1)^{2} = x - 2020

展开

4 (5 x + 1)^{2} : 100 x^{2} + 40 x + 4

100 x^{2} + 40 x + 4 = x - 2020

将

2020

para o lado esquerdo

100 x^{2} + 40 x + 2024 = x

将

x

para o lado esquerdo

100 x^{2} + 39 x + 2024 = 0

使用求根公式求解

x_{1, 2} = \frac{- 39 \pm 3 9 ^{2} - 4 \cdot 100 \cdot 2024}{2 \cdot 100}

化简

3 9^{2} - 4 \cdot 100 \cdot 2024 : 808079 i

x_{1, 2} = \frac{- 39 \pm 808079 i}{2 \cdot 100}

将解分隔开

x_{1} = \frac{- 39 + 808079 i}{2 \cdot 100}, x_{2} = \frac{- 39 - 808079 i}{2 \cdot 100}

x = \frac{- 39 + 808079 i}{2 \cdot 100} : - \frac{39}{200} + i \frac{808079}{200}

x = \frac{- 39 - 808079 i}{2 \cdot 100} : - \frac{39}{200} - i \frac{808079}{200}

二次方程组的解是:

x = - \frac{39}{200} + i \frac{808079}{200}, x = - \frac{39}{200} - i \frac{808079}{200}

作图

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