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受欢迎的代数 >

3(x-3)(x+5)=7x^2+2x-3

解答

3 (x - 3) (x + 5) = 7 x^{2} + 2 x - 3

解答

x = \frac{1}{2} - i \frac{41}{2}, x = \frac{1}{2} + i \frac{41}{2}

求解步骤

3 (x - 3) (x + 5) = 7 x^{2} + 2 x - 3

展开

3 (x - 3) (x + 5) : 3 x^{2} + 6 x - 45

3 x^{2} + 6 x - 45 = 7 x^{2} + 2 x - 3

将

3

para o lado esquerdo

3 x^{2} + 6 x - 42 = 7 x^{2} + 2 x

将

2 x

para o lado esquerdo

3 x^{2} + 4 x - 42 = 7 x^{2}

将

7 x^{2}

para o lado esquerdo

- 4 x^{2} + 4 x - 42 = 0

使用求根公式求解

x_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 ( - 4 ) ( - 42 )}{2 ( - 4 )}

化简

4^{2} - 4 (- 4) (- 42) : 441 i

x_{1, 2} = \frac{- 4 \pm 4 41 i}{2 ( - 4 )}

将解分隔开

x_{1} = \frac{- 4 + 4 41 i}{2 ( - 4 )}, x_{2} = \frac{- 4 - 4 41 i}{2 ( - 4 )}

x = \frac{- 4 + 4 41 i}{2 ( - 4 )} : \frac{1}{2} - i \frac{41}{2}

x = \frac{- 4 - 4 41 i}{2 ( - 4 )} : \frac{1}{2} + i \frac{41}{2}

二次方程组的解是:

x = \frac{1}{2} - i \frac{41}{2}, x = \frac{1}{2} + i \frac{41}{2}

作图

流行的例子

- 2 x + 8 = - 9 x^{2}

x^{2} - 10 x = 1575

4 m^{2} - 19 m + 20 = 0

2 x (x + 3) = - 2

(x - 4)^{2} = 3 x - 12