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受欢迎的代数 >

(8× 10^{-3})(2.71775-1950x)^2-x=0

解答

(8 \cdot 1 0^{- 3}) (2.71775 - 1950 x)^{2} - x = 0

解答

x = \frac{10724.225 + 3802500 \frac{115009001.850625}{380250 0 ^{2}} - \frac{29.54466 \dots}{3802500}}{7605000}, x = \frac{10724.225 - 3802500 \frac{115009001.850625}{380250 0 ^{2}} - \frac{29.54466 \dots}{3802500}}{7605000}

+1

十进制

x = 0.00162 \dots, x = 0.00119 \dots

求解步骤

(8 \cdot 1 0^{- 3}) (2.71775 - 1950 x)^{2} - x = 0

展开

(8 \cdot 1 0^{- 3}) (2.71775 - 1950 x)^{2} - x : 30420 x^{2} - \frac{10724.225 x}{125} + \frac{7.38616 \dots}{125}

30420 x^{2} - \frac{10724.225 x}{125} + \frac{7.38616 \dots}{125} = 0

两边除以

30420

\frac{30420 x ^{2}}{30420} - \frac{\frac{10724.225 x}{125}}{30420} + \frac{\frac{7.38616 \dots}{125}}{30420} = \frac{0}{30420}

改写成标准形式

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

x^{2} - \frac{10724.225 x}{3802500} + \frac{7.38616 \dots}{3802500} = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - \frac{10724.225}{3802500} ) \pm ( - \frac{10724.225}{3802500} ) ^{2} - 4 \cdot 1 \cdot \frac{7.38616 \dots}{3802500}}{2 \cdot 1}

(- \frac{10724.225}{3802500})^{2} - 4 \cdot 1 \cdot \frac{7.38616 \dots}{3802500} = \frac{115009001.850625}{380250 0 ^{2}} - \frac{29.54466 \dots}{3802500}

x_{1, 2} = \frac{- ( - \frac{10724.225}{3802500} ) \pm \frac{115009001.850625}{380250 0 ^{2}} - \frac{29.54466 \dots}{3802500}}{2 \cdot 1}

将解分隔开

x_{1} = \frac{- ( - \frac{10724.225}{3802500} ) + \frac{115009001.850625}{380250 0 ^{2}} - \frac{29.54466 \dots}{3802500}}{2 \cdot 1}, x_{2} = \frac{- ( - \frac{10724.225}{3802500} ) - \frac{115009001.850625}{380250 0 ^{2}} - \frac{29.54466 \dots}{3802500}}{2 \cdot 1}

x = \frac{- ( - \frac{10724.225}{3802500} ) + \frac{115009001.850625}{380250 0 ^{2}} - \frac{29.54466 \dots}{3802500}}{2 \cdot 1} : \frac{10724.225 + 3802500 \frac{115009001.850625}{380250 0 ^{2}} - \frac{29.54466 \dots}{3802500}}{7605000}

x = \frac{- ( - \frac{10724.225}{3802500} ) - \frac{115009001.850625}{380250 0 ^{2}} - \frac{29.54466 \dots}{3802500}}{2 \cdot 1} : \frac{10724.225 - 3802500 \frac{115009001.850625}{380250 0 ^{2}} - \frac{29.54466 \dots}{3802500}}{7605000}

二次方程组的解是:

x = \frac{10724.225 + 3802500 \frac{115009001.850625}{380250 0 ^{2}} - \frac{29.54466 \dots}{3802500}}{7605000}, x = \frac{10724.225 - 3802500 \frac{115009001.850625}{380250 0 ^{2}} - \frac{29.54466 \dots}{3802500}}{7605000}

作图

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