solvefor x,5x^2+5kx+80=0

解

x, 5 x^{2} + 5 k x + 80 = 0

x = \frac{- k + k ^{2} - 64}{2}, x = - \frac{k + k ^{2} - 64}{2}

解答ステップ

5 x^{2} + 5 k x + 80 = 0

解くとthe二次式

x_{1, 2} = \frac{- 5 k \pm ( 5 k ) ^{2} - 4 \cdot 5 \cdot 80}{2 \cdot 5}

簡素化

(5 k)^{2} - 4 \cdot 5 \cdot 80 : 5 k^{2} - 64

x_{1, 2} = \frac{- 5 k \pm 5 k ^{2} - 64}{2 \cdot 5}

解を分離する

x_{1} = \frac{- 5 k + 5 k ^{2} - 64}{2 \cdot 5}, x_{2} = \frac{- 5 k - 5 k ^{2} - 64}{2 \cdot 5}

x = \frac{- 5 k + 5 k ^{2} - 64}{2 \cdot 5} : \frac{- k + k ^{2} - 64}{2}

x = \frac{- 5 k - 5 k ^{2} - 64}{2 \cdot 5} : - \frac{k + k ^{2} - 64}{2}

二次equationの解:

x = \frac{- k + k ^{2} - 64}{2}, x = - \frac{k + k ^{2} - 64}{2}