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受欢迎的代数 >

(0.75*10^4)x=(-3000x+15-1)^2

解答

(0.75 \cdot 1 0^{4}) x = (- 3000 x + 15 - 1)^{2}

解答

x = \frac{61 5 + 15 13}{12000 5}, x = \frac{61 5 - 15 13}{12000 5}

+1

十进制

x = 0.00709 \dots, x = 0.00306 \dots

求解步骤

(0.75 \cdot 1 0^{4}) x = (- 3000 x + 15 - 1)^{2}

展开

(0.75 \cdot 1 0^{4}) x : 7500 x

展开

(- 3000 x + 15 - 1)^{2} : 9000000 x^{2} - 84000 x + 196

7500 x = 9000000 x^{2} - 84000 x + 196

交换两边

9000000 x^{2} - 84000 x + 196 = 7500 x

将

7500 x

para o lado esquerdo

9000000 x^{2} - 91500 x + 196 = 0

两边除以

9000000

\frac{9000000 x ^{2}}{9000000} - \frac{91500 x}{9000000} + \frac{196}{9000000} = \frac{0}{9000000}

改写成标准形式

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

x^{2} - \frac{61 x}{6000} + \frac{49}{2250000} = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - \frac{61}{6000} ) \pm ( - \frac{61}{6000} ) ^{2} - 4 \cdot 1 \cdot \frac{49}{2250000}}{2 \cdot 1}

(- \frac{61}{6000})^{2} - 4 \cdot 1 \cdot \frac{49}{2250000} = \frac{13}{400 5}

x_{1, 2} = \frac{- ( - \frac{61}{6000} ) \pm \frac{13}{400 5}}{2 \cdot 1}

将解分隔开

x_{1} = \frac{- ( - \frac{61}{6000} ) + \frac{13}{400 5}}{2 \cdot 1}, x_{2} = \frac{- ( - \frac{61}{6000} ) - \frac{13}{400 5}}{2 \cdot 1}

x = \frac{- ( - \frac{61}{6000} ) + \frac{13}{400 5}}{2 \cdot 1} : \frac{61 5 + 15 13}{12000 5}

x = \frac{- ( - \frac{61}{6000} ) - \frac{13}{400 5}}{2 \cdot 1} : \frac{61 5 - 15 13}{12000 5}

二次方程组的解是:

x = \frac{61 5 + 15 13}{12000 5}, x = \frac{61 5 - 15 13}{12000 5}

作图

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