quadraticformula 2x^2+5x+20=0

解

2 x^{2} + 5 x + 20 = 0

x = - \frac{5}{4} + i \frac{3 15}{4}, x = - \frac{5}{4} - i \frac{3 15}{4}

解答ステップ

2 x^{2} + 5 x + 20 = 0

解くとthe二次式

x_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 2 \cdot 20}{2 \cdot 2}

簡素化

5^{2} - 4 \cdot 2 \cdot 20 : 315 i

x_{1, 2} = \frac{- 5 \pm 3 15 i}{2 \cdot 2}

解を分離する

x_{1} = \frac{- 5 + 3 15 i}{2 \cdot 2}, x_{2} = \frac{- 5 - 3 15 i}{2 \cdot 2}

x = \frac{- 5 + 3 15 i}{2 \cdot 2} : - \frac{5}{4} + i \frac{3 15}{4}

x = \frac{- 5 - 3 15 i}{2 \cdot 2} : - \frac{5}{4} - i \frac{3 15}{4}

二次equationの解:

x = - \frac{5}{4} + i \frac{3 15}{4}, x = - \frac{5}{4} - i \frac{3 15}{4}