10x^2+(20k+50)x+10k=0

解

10 x^{2} + (20 k + 50) x + 10 k = 0

x = \frac{- 2 k - 5 + 4 k ^{2} + 16 k + 25}{2}, x = - \frac{2 k + 4 k ^{2} + 16 k + 25 + 5}{2}

解答ステップ

10 x^{2} + (20 k + 50) x + 10 k = 0

解くとthe二次式

x_{1, 2} = \frac{- ( 20 k + 50 ) \pm ( 20 k + 50 ) ^{2} - 4 \cdot 10 \cdot 10 k}{2 \cdot 10}

簡素化

(20 k + 50)^{2} - 4 \cdot 10 \cdot 10 k : 10 4 k^{2} + 16 k + 25

x_{1, 2} = \frac{- ( 20 k + 50 ) \pm 10 4 k ^{2} + 16 k + 25}{2 \cdot 10}

解を分離する

x_{1} = \frac{- ( 20 k + 50 ) + 10 4 k ^{2} + 16 k + 25}{2 \cdot 10}, x_{2} = \frac{- ( 20 k + 50 ) - 10 4 k ^{2} + 16 k + 25}{2 \cdot 10}

x = \frac{- ( 20 k + 50 ) + 10 4 k ^{2} + 16 k + 25}{2 \cdot 10} : \frac{- 2 k - 5 + 4 k ^{2} + 16 k + 25}{2}

x = \frac{- ( 20 k + 50 ) - 10 4 k ^{2} + 16 k + 25}{2 \cdot 10} : - \frac{2 k + 4 k ^{2} + 16 k + 25 + 5}{2}

二次equationの解:

x = \frac{- 2 k - 5 + 4 k ^{2} + 16 k + 25}{2}, x = - \frac{2 k + 4 k ^{2} + 16 k + 25 + 5}{2}