(m+5)x^2+3mx+m=0

解

(m + 5) x^{2} + 3 m x + m = 0

x = \frac{- 3 m + 5 m ^{2} - 20 m}{2 ( m + 5 )}, x = \frac{- 3 m - 5 m ^{2} - 20 m}{2 ( m + 5 )}; m \neq = - 5

解答ステップ

(m + 5) x^{2} + 3 m x + m = 0

解くとthe二次式

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

簡素化

(3 m)^{2} - 4 (m + 5) m : 5 m^{2} - 20 m

x_{1, 2} = \frac{- 3 m \pm 5 m ^{2} - 20 m}{2 ( m + 5 )}; m \neq = - 5

解を分離する

x_{1} = \frac{- 3 m + 5 m ^{2} - 20 m}{2 ( m + 5 )}, x_{2} = \frac{- 3 m - 5 m ^{2} - 20 m}{2 ( m + 5 )}

x = \frac{- 3 m + 5 m ^{2} - 20 m}{2 ( m + 5 )}; m \neq = - 5

x = \frac{- 3 m - 5 m ^{2} - 20 m}{2 ( m + 5 )}; m \neq = - 5

二次equationの解:

x = \frac{- 3 m + 5 m ^{2} - 20 m}{2 ( m + 5 )}, x = \frac{- 3 m - 5 m ^{2} - 20 m}{2 ( m + 5 )}; m \neq = - 5