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人気のある代数 >

(3-x)/(1000)=(4010)/(21)(3-x-0.7)^2

解

\frac{3 - x}{1000} = \frac{40 \cdot 10}{2 \cdot 1} (3 - x - 0.7)^{2}

解

x = \frac{919999 + 200000 \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{400000}, x = \frac{919999 - 200000 \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{400000}

+1

十進法表記

x = 2.30186 \dots, x = 2.29812 \dots

解答ステップ

\frac{3 - x}{1000} = \frac{40 \cdot 10}{2 \cdot 1} (3 - x - 0.7)^{2}

以下の最小公倍数を求める:

1000, 2 : 1000

以下で乗じる: LCM=

1000

\frac{3 - x}{1000} \cdot 1000 = \frac{40 \cdot 10}{2 \cdot 1} (3 - x - 0.7)^{2} \cdot 1000

簡素化

3 - x = 200000 (- x + 2.3)^{2}

拡張

200000 (- x + 2.3)^{2} : 200000 x^{2} - 920000 x + 1058000

3 - x = 200000 x^{2} - 920000 x + 1058000

辺を交換する

200000 x^{2} - 920000 x + 1058000 = 3 - x

x

を左側に移動します

200000 x^{2} - 919999 x + 1058000 = 3

3

を左側に移動します

200000 x^{2} - 919999 x + 1057997 = 0

以下で両辺を割る

200000

\frac{200000 x ^{2}}{200000} - \frac{919999 x}{200000} + \frac{1057997}{200000} = \frac{0}{200000}

標準的な形式で書く

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

x^{2} - \frac{919999 x}{200000} + \frac{1057997}{200000} = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - \frac{919999}{200000} ) \pm ( - \frac{919999}{200000} ) ^{2} - 4 \cdot 1 \cdot \frac{1057997}{200000}}{2 \cdot 1}

(- \frac{919999}{200000})^{2} - 4 \cdot 1 \cdot \frac{1057997}{200000} = \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}

x_{1, 2} = \frac{- ( - \frac{919999}{200000} ) \pm \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{2 \cdot 1}

解を分離する

x_{1} = \frac{- ( - \frac{919999}{200000} ) + \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{2 \cdot 1}, x_{2} = \frac{- ( - \frac{919999}{200000} ) - \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{2 \cdot 1}

x = \frac{- ( - \frac{919999}{200000} ) + \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{2 \cdot 1} : \frac{919999 + 200000 \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{400000}

x = \frac{- ( - \frac{919999}{200000} ) - \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{2 \cdot 1} : \frac{919999 - 200000 \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{400000}

二次equationの解:

x = \frac{919999 + 200000 \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{400000}, x = \frac{919999 - 200000 \frac{91999 9 ^{2}}{20000 0 ^{2}} - \frac{1057997}{50000}}{400000}

グラフ

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