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受欢迎的代数 >

50x-49/40 x^2=80(x+2)+1/2*(-9.8)(x+2)^2

解答

50 x - \frac{49}{40} x^{2} = 80 (x + 2) + \frac{1}{2} \cdot (- 9.8) (x + 2)^{2}

解答

x = - \frac{4 ( 54301 - 52 )}{147}, x = \frac{4 ( 52 + 54301 )}{147}

+1

十进制

x = - 4.92587 \dots, x = 7.75580 \dots

求解步骤

50 x - \frac{49}{40} x^{2} = 80 (x + 2) + \frac{1}{2} (- 9.8) (x + 2)^{2}

找到

40, 2

的最小公倍数:

40

乘以最小公倍数=

40

50 x \cdot 40 - \frac{49}{40} x^{2} \cdot 40 = 80 (x + 2) \cdot 40 + \frac{1}{2} (- 9.8) (x + 2)^{2} \cdot 40

化简

2000 x - 49 x^{2} = 3200 (x + 2) - 196 (x + 2)^{2}

展开

3200 (x + 2) - 196 (x + 2)^{2} : - 196 x^{2} + 2416 x + 5616

2000 x - 49 x^{2} = - 196 x^{2} + 2416 x + 5616

交换两边

- 196 x^{2} + 2416 x + 5616 = 2000 x - 49 x^{2}

将

49 x^{2}

para o lado esquerdo

- 147 x^{2} + 2416 x + 5616 = 2000 x

将

2000 x

para o lado esquerdo

- 147 x^{2} + 416 x + 5616 = 0

使用求根公式求解

x_{1, 2} = \frac{- 416 \pm 41 6 ^{2} - 4 ( - 147 ) \cdot 5616}{2 ( - 147 )}

41 6^{2} - 4 (- 147) \cdot 5616 = 854301

x_{1, 2} = \frac{- 416 \pm 8 54301}{2 ( - 147 )}

将解分隔开

x_{1} = \frac{- 416 + 8 54301}{2 ( - 147 )}, x_{2} = \frac{- 416 - 8 54301}{2 ( - 147 )}

x = \frac{- 416 + 8 54301}{2 ( - 147 )} : - \frac{4 ( 54301 - 52 )}{147}

x = \frac{- 416 - 8 54301}{2 ( - 147 )} : \frac{4 ( 52 + 54301 )}{147}

二次方程组的解是:

x = - \frac{4 ( 54301 - 52 )}{147}, x = \frac{4 ( 52 + 54301 )}{147}

作图

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