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人気のある代数 >

x^2-x(b-a)=(a+x)(b-x)

解

x^{2} - x (b - a) = (a + x) (b - x)

解

x = - \frac{- b + a + b ^{2} + a ^{2}}{2}, x = - \frac{- b + a - b ^{2} + a ^{2}}{2}

解答ステップ

x^{2} - x (b - a) = (a + x) (b - x)

拡張

x^{2} - x (b - a) : x^{2} - b x + a x

拡張

(a + x) (b - x) : ba - a x + b x - x^{2}

x^{2} - b x + a x = ba - a x + b x - x^{2}

辺を交換する

ba - a x + b x - x^{2} = x^{2} - b x + a x

a x

を左側に移動します

- x^{2} + b x - 2 a x + ba = x^{2} - b x

b x

を左側に移動します

- x^{2} + 2 b x - 2 a x + ba = x^{2}

x^{2}

を左側に移動します

- 2 x^{2} + 2 b x - 2 a x + ba = 0

標準的な形式で書く

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

- 2 x^{2} + (2 b - 2 a) x + ba = 0

解くとthe二次式

x_{1, 2} = \frac{- ( 2 b - 2 a ) \pm ( 2 b - 2 a ) ^{2} - 4 ( - 2 ) ba}{2 ( - 2 )}

簡素化

(2 b - 2 a)^{2} - 4 (- 2) ba : 2 b^{2} + a^{2}

x_{1, 2} = \frac{- ( 2 b - 2 a ) \pm 2 b ^{2} + a ^{2}}{2 ( - 2 )}

解を分離する

x_{1} = \frac{- ( 2 b - 2 a ) + 2 b ^{2} + a ^{2}}{2 ( - 2 )}, x_{2} = \frac{- ( 2 b - 2 a ) - 2 b ^{2} + a ^{2}}{2 ( - 2 )}

x = \frac{- ( 2 b - 2 a ) + 2 b ^{2} + a ^{2}}{2 ( - 2 )} : - \frac{- b + a + b ^{2} + a ^{2}}{2}

x = \frac{- ( 2 b - 2 a ) - 2 b ^{2} + a ^{2}}{2 ( - 2 )} : - \frac{- b + a - b ^{2} + a ^{2}}{2}

二次equationの解:

x = - \frac{- b + a + b ^{2} + a ^{2}}{2}, x = - \frac{- b + a - b ^{2} + a ^{2}}{2}

グラフ

人気の例

- 8 x^{2} = - 800

x^{2} + 5 x = - 3

- x^{2} + 18 x - 81 = 0

((x-3)^2)/(25)=0

\frac{( x - 3 ) ^{2}}{25} = 0

t^{2} + 30 t = - 17