(m+1)x^2+(2m+3)x-14=0

解

(m + 1) x^{2} + (2 m + 3) x - 14 = 0

x = \frac{- 2 m - 3 + 4 m ^{2} + 68 m + 65}{2 ( m + 1 )}, x = \frac{- 2 m - 3 - 4 m ^{2} + 68 m + 65}{2 ( m + 1 )}; m \neq = - 1

解答ステップ

(m + 1) x^{2} + (2 m + 3) x - 14 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( 2 m + 3 ) \pm ( 2 m + 3 ) ^{2} - 4 ( m + 1 ) ( - 14 )}{2 ( m + 1 )}

簡素化

(2 m + 3)^{2} - 4 (m + 1) (- 14) : 4 m^{2} + 68 m + 65

x_{1, 2} = \frac{- ( 2 m + 3 ) \pm 4 m ^{2} + 68 m + 65}{2 ( m + 1 )}; m \neq = - 1

解を分離する

x_{1} = \frac{- ( 2 m + 3 ) + 4 m ^{2} + 68 m + 65}{2 ( m + 1 )}, x_{2} = \frac{- ( 2 m + 3 ) - 4 m ^{2} + 68 m + 65}{2 ( m + 1 )}

x = \frac{- ( 2 m + 3 ) + 4 m ^{2} + 68 m + 65}{2 ( m + 1 )} : \frac{- 2 m - 3 + 4 m ^{2} + 68 m + 65}{2 ( m + 1 )}

x = \frac{- ( 2 m + 3 ) - 4 m ^{2} + 68 m + 65}{2 ( m + 1 )} : \frac{- 2 m - 3 - 4 m ^{2} + 68 m + 65}{2 ( m + 1 )}

二次equationの解:

x = \frac{- 2 m - 3 + 4 m ^{2} + 68 m + 65}{2 ( m + 1 )}, x = \frac{- 2 m - 3 - 4 m ^{2} + 68 m + 65}{2 ( m + 1 )}; m \neq = - 1