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人気のある代数 >

(2a+1)x^2+(-5a-10)x+(3a-1)=0

解

(2 a + 1) x^{2} + (- 5 a - 10) x + (3 a - 1) = 0

解

x = \frac{5 a + 10 + a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}, x = \frac{5 a + 10 - a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}; a \neq = - \frac{1}{2}

解答ステップ

(2 a + 1) x^{2} + (- 5 a - 10) x + (3 a - 1) = 0

拡張

(2 a + 1) x^{2} + (- 5 a - 10) x + (3 a - 1) : 2 a x^{2} + x^{2} - 5 a x - 10 x + 3 a - 1

2 a x^{2} + x^{2} - 5 a x - 10 x + 3 a - 1 = 0

標準的な形式で書く

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

(2 a + 1) x^{2} - (5 a + 10) x + 3 a - 1 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 5 a - 10 ) \pm ( - 5 a - 10 ) ^{2} - 4 ( 2 a + 1 ) ( 3 a - 1 )}{2 ( 2 a + 1 )}

簡素化

(- 5 a - 10)^{2} - 4 (2 a + 1) (3 a - 1) : a^{2} + 96 a + 104

x_{1, 2} = \frac{- ( - 5 a - 10 ) \pm a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}; a \neq = - \frac{1}{2}

解を分離する

x_{1} = \frac{- ( - 5 a - 10 ) + a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}, x_{2} = \frac{- ( - 5 a - 10 ) - a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}

x = \frac{- ( - 5 a - 10 ) + a ^{2} + 96 a + 104}{2 ( 2 a + 1 )} : \frac{5 a + 10 + a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}

x = \frac{- ( - 5 a - 10 ) - a ^{2} + 96 a + 104}{2 ( 2 a + 1 )} : \frac{5 a + 10 - a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}

二次equationの解:

x = \frac{5 a + 10 + a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}, x = \frac{5 a + 10 - a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}; a \neq = - \frac{1}{2}

グラフ

人気の例

3x^2-15x-8=-10x

3 x^{2} - 15 x - 8 = - 10 x

2 k^{2} + 5 k - 11 = 1

15 a^{2} - 8 a - 3 = - 4

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6 k^{2} + 6 k - 6 = k