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人気のある代数 >

((a-1)x+2a-1)x+3ax=2a-3

解

((a - 1) x + 2 a - 1) x + 3 a x = 2 a - 3

解

x = \frac{- 5 a + 1 + 33 a ^{2} - 30 a + 13}{2 ( a - 1 )}, x = \frac{- 5 a + 1 - 33 a ^{2} - 30 a + 13}{2 ( a - 1 )}; a \neq = 1

解答ステップ

((a - 1) x + 2 a - 1) x + 3 a x = 2 a - 3

拡張

((a - 1) x + 2 a - 1) x + 3 a x : a x^{2} - x^{2} + 5 a x - x

a x^{2} - x^{2} + 5 a x - x = 2 a - 3

3

を左側に移動します

a x^{2} - x^{2} + 5 a x - x + 3 = 2 a

2 a

を左側に移動します

a x^{2} - x^{2} + 5 a x - x + 3 - 2 a = 0

標準的な形式で書く

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

(a - 1) x^{2} + (5 a - 1) x + 3 - 2 a = 0

解くとthe二次式

x_{1, 2} = \frac{- ( 5 a - 1 ) \pm ( 5 a - 1 ) ^{2} - 4 ( a - 1 ) ( 3 - 2 a )}{2 ( a - 1 )}

簡素化

(5 a - 1)^{2} - 4 (a - 1) (3 - 2 a) : 33 a^{2} - 30 a + 13

x_{1, 2} = \frac{- ( 5 a - 1 ) \pm 33 a ^{2} - 30 a + 13}{2 ( a - 1 )}; a \neq = 1

解を分離する

x_{1} = \frac{- ( 5 a - 1 ) + 33 a ^{2} - 30 a + 13}{2 ( a - 1 )}, x_{2} = \frac{- ( 5 a - 1 ) - 33 a ^{2} - 30 a + 13}{2 ( a - 1 )}

x = \frac{- ( 5 a - 1 ) + 33 a ^{2} - 30 a + 13}{2 ( a - 1 )} : \frac{- 5 a + 1 + 33 a ^{2} - 30 a + 13}{2 ( a - 1 )}

x = \frac{- ( 5 a - 1 ) - 33 a ^{2} - 30 a + 13}{2 ( a - 1 )} : \frac{- 5 a + 1 - 33 a ^{2} - 30 a + 13}{2 ( a - 1 )}

二次equationの解:

x = \frac{- 5 a + 1 + 33 a ^{2} - 30 a + 13}{2 ( a - 1 )}, x = \frac{- 5 a + 1 - 33 a ^{2} - 30 a + 13}{2 ( a - 1 )}; a \neq = 1

グラフ

人気の例

-3(2x-5)^2+13=4

- 3 (2 x - 5)^{2} + 13 = 4

r^{2} - 3 r = 10

w^{2} + 13 w + 42 = 0

4 0^{2} + x^{2} = 4 1^{2}

3 m^{2} + 5 m = 6