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人気のある代数 >

10x^2+19x+6=(5x+a)(bx+c)

解

10 x^{2} + 19 x + 6 = (5 x + a) (b x + c)

解

x = \frac{- 19 + ab + 5 c + a ^{2} b ^{2} + 40 a c - 38 ab - 10 ab c + 120 b + 25 c ^{2} + 121 - 190 c}{2 ( 10 - 5 b )}, x = \frac{- 19 + ab + 5 c - a ^{2} b ^{2} + 40 a c - 38 ab - 10 ab c + 120 b + 25 c ^{2} + 121 - 190 c}{2 ( 10 - 5 b )}; b \neq = 2

解答ステップ

10 x^{2} + 19 x + 6 = (5 x + a) (b x + c)

拡張

(5 x + a) (b x + c) : 5 b x^{2} + 5 c x + ab x + a c

10 x^{2} + 19 x + 6 = 5 b x^{2} + 5 c x + ab x + a c

両辺から

ab x + a c

を引く

10 x^{2} + 19 x + 6 - (ab x + a c) = 5 b x^{2} + 5 c x + ab x + a c - (ab x + a c)

簡素化

10 x^{2} + 19 x + 6 - ab x - a c = 5 b x^{2} + 5 c x

5 c x

を左側に移動します

10 x^{2} + 19 x + 6 - ab x - a c - 5 c x = 5 b x^{2}

5 b x^{2}

を左側に移動します

10 x^{2} + 19 x + 6 - ab x - a c - 5 c x - 5 b x^{2} = 0

標準的な形式で書く

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

(10 - 5 b) x^{2} + (19 - ab - 5 c) x + 6 - a c = 0

解くとthe二次式

x_{1, 2} = \frac{- ( 19 - ab - 5 c ) \pm ( 19 - ab - 5 c ) ^{2} - 4 ( 10 - 5 b ) ( 6 - a c )}{2 ( 10 - 5 b )}

簡素化

(19 - ab - 5 c)^{2} - 4 (10 - 5 b) (6 - a c) : a^{2} b^{2} + 40 a c - 38 ab - 10 ab c + 120 b + 25 c^{2} + 121 - 190 c

x_{1, 2} = \frac{- ( 19 - ab - 5 c ) \pm a ^{2} b ^{2} + 40 a c - 38 ab - 10 ab c + 120 b + 25 c ^{2} + 121 - 190 c}{2 ( 10 - 5 b )}; b \neq = 2

解を分離する

x_{1} = \frac{- ( 19 - ab - 5 c ) + a ^{2} b ^{2} + 40 a c - 38 ab - 10 ab c + 120 b + 25 c ^{2} + 121 - 190 c}{2 ( 10 - 5 b )}, x_{2} = \frac{- ( 19 - ab - 5 c ) - a ^{2} b ^{2} + 40 a c - 38 ab - 10 ab c + 120 b + 25 c ^{2} + 121 - 190 c}{2 ( 10 - 5 b )}

x = \frac{- ( 19 - ab - 5 c ) + a ^{2} b ^{2} + 40 a c - 38 ab - 10 ab c + 120 b + 25 c ^{2} + 121 - 190 c}{2 ( 10 - 5 b )} : \frac{- 19 + ab + 5 c + a ^{2} b ^{2} + 40 a c - 38 ab - 10 ab c + 120 b + 25 c ^{2} + 121 - 190 c}{2 ( 10 - 5 b )}

x = \frac{- ( 19 - ab - 5 c ) - a ^{2} b ^{2} + 40 a c - 38 ab - 10 ab c + 120 b + 25 c ^{2} + 121 - 190 c}{2 ( 10 - 5 b )} : \frac{- 19 + ab + 5 c - a ^{2} b ^{2} + 40 a c - 38 ab - 10 ab c + 120 b + 25 c ^{2} + 121 - 190 c}{2 ( 10 - 5 b )}

二次equationの解:

x = \frac{- 19 + ab + 5 c + a ^{2} b ^{2} + 40 a c - 38 ab - 10 ab c + 120 b + 25 c ^{2} + 121 - 190 c}{2 ( 10 - 5 b )}, x = \frac{- 19 + ab + 5 c - a ^{2} b ^{2} + 40 a c - 38 ab - 10 ab c + 120 b + 25 c ^{2} + 121 - 190 c}{2 ( 10 - 5 b )}; b \neq = 2

グラフ

人気の例

- 4 x^{2} + 8 x - 4 = 0

- 3 x^{2} - 4 = 0

0.000006x^2-0.02x+25=15

0.000006 x^{2} - 0.02 x + 25 = 15

(2x+1)(x-1)=-16x-8

(2 x + 1) (x - 1) = - 16 x - 8

a^{2} + 64 = 100