8x^2+(3k-4)x+7=0

解

8 x^{2} + (3 k - 4) x + 7 = 0

x = \frac{- 3 k + 4 + 9 k ^{2} - 24 k - 208}{16}, x = \frac{- 3 k + 4 - 9 k ^{2} - 24 k - 208}{16}

解答ステップ

8 x^{2} + (3 k - 4) x + 7 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( 3 k - 4 ) \pm ( 3 k - 4 ) ^{2} - 4 \cdot 8 \cdot 7}{2 \cdot 8}

簡素化

(3 k - 4)^{2} - 4 \cdot 8 \cdot 7 : 9 k^{2} - 24 k - 208

x_{1, 2} = \frac{- ( 3 k - 4 ) \pm 9 k ^{2} - 24 k - 208}{2 \cdot 8}

解を分離する

x_{1} = \frac{- ( 3 k - 4 ) + 9 k ^{2} - 24 k - 208}{2 \cdot 8}, x_{2} = \frac{- ( 3 k - 4 ) - 9 k ^{2} - 24 k - 208}{2 \cdot 8}

x = \frac{- ( 3 k - 4 ) + 9 k ^{2} - 24 k - 208}{2 \cdot 8} : \frac{- 3 k + 4 + 9 k ^{2} - 24 k - 208}{16}

x = \frac{- ( 3 k - 4 ) - 9 k ^{2} - 24 k - 208}{2 \cdot 8} : \frac{- 3 k + 4 - 9 k ^{2} - 24 k - 208}{16}

二次equationの解:

x = \frac{- 3 k + 4 + 9 k ^{2} - 24 k - 208}{16}, x = \frac{- 3 k + 4 - 9 k ^{2} - 24 k - 208}{16}