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人気のある代数 >

(2x+1)(x+3)=ax^2+bx+c

解

(2 x + 1) (x + 3) = a x^{2} + b x + c

解

x = \frac{- 7 + b + 12 a - 4 a c + b ^{2} + 8 c + 25 - 14 b}{2 ( 2 - a )}, x = \frac{- 7 + b - 12 a - 4 a c + b ^{2} + 8 c + 25 - 14 b}{2 ( 2 - a )}; a \neq = 2

解答ステップ

(2 x + 1) (x + 3) = a x^{2} + b x + c

拡張

(2 x + 1) (x + 3) : 2 x^{2} + 7 x + 3

2 x^{2} + 7 x + 3 = a x^{2} + b x + c

c

を左側に移動します

2 x^{2} + 7 x + 3 - c = a x^{2} + b x

b x

を左側に移動します

2 x^{2} + 7 x + 3 - c - b x = a x^{2}

a x^{2}

を左側に移動します

2 x^{2} + 7 x + 3 - c - b x - a x^{2} = 0

標準的な形式で書く

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

(2 - a) x^{2} + (7 - b) x + 3 - c = 0

解くとthe二次式

x_{1, 2} = \frac{- ( 7 - b ) \pm ( 7 - b ) ^{2} - 4 ( 2 - a ) ( 3 - c )}{2 ( 2 - a )}

簡素化

(7 - b)^{2} - 4 (2 - a) (3 - c) : 12 a - 4 a c + b^{2} + 8 c + 25 - 14 b

x_{1, 2} = \frac{- ( 7 - b ) \pm 12 a - 4 a c + b ^{2} + 8 c + 25 - 14 b}{2 ( 2 - a )}; a \neq = 2

解を分離する

x_{1} = \frac{- ( 7 - b ) + 12 a - 4 a c + b ^{2} + 8 c + 25 - 14 b}{2 ( 2 - a )}, x_{2} = \frac{- ( 7 - b ) - 12 a - 4 a c + b ^{2} + 8 c + 25 - 14 b}{2 ( 2 - a )}

x = \frac{- ( 7 - b ) + 12 a - 4 a c + b ^{2} + 8 c + 25 - 14 b}{2 ( 2 - a )} : \frac{- 7 + b + 12 a - 4 a c + b ^{2} + 8 c + 25 - 14 b}{2 ( 2 - a )}

x = \frac{- ( 7 - b ) - 12 a - 4 a c + b ^{2} + 8 c + 25 - 14 b}{2 ( 2 - a )} : \frac{- 7 + b - 12 a - 4 a c + b ^{2} + 8 c + 25 - 14 b}{2 ( 2 - a )}

二次equationの解:

x = \frac{- 7 + b + 12 a - 4 a c + b ^{2} + 8 c + 25 - 14 b}{2 ( 2 - a )}, x = \frac{- 7 + b - 12 a - 4 a c + b ^{2} + 8 c + 25 - 14 b}{2 ( 2 - a )}; a \neq = 2

グラフ

人気の例

c (x) = 4 x^{2} + 3 x + 6

16 = x^{2} - 6 x

6 t^{2} + 14 = - 25 t

0 = 4800 - \frac{3}{4} x^{2}

5 x^{2} - 12 x = - 3