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受欢迎的代数 >

x^2=-2(2x+1)

解答

x^{2} = - 2 (2 x + 1)

解答

x = - 2 + 2, x = - 2 - 2

+1

十进制

x = - 0.58578 \dots, x = - 3.41421 \dots

求解步骤

x^{2} = - 2 (2 x + 1)

展开

- 2 (2 x + 1) : - 4 x - 2

x^{2} = - 4 x - 2

将

2

para o lado esquerdo

x^{2} + 2 = - 4 x

将

4 x

para o lado esquerdo

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

改写成标准形式

a x^{2} + b x + c = 0

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

使用求根公式求解

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

4^{2} - 4 \cdot 1 \cdot 2 = 22

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

将解分隔开

x_{1} = \frac{- 4 + 2 2}{2 \cdot 1}, x_{2} = \frac{- 4 - 2 2}{2 \cdot 1}

x = \frac{- 4 + 2 2}{2 \cdot 1} : - 2 + 2

x = \frac{- 4 - 2 2}{2 \cdot 1} : - 2 - 2

二次方程组的解是:

x = - 2 + 2, x = - 2 - 2

作图

流行的例子

x^{2} - \frac{3}{4} x = - \frac{1}{4}

8 t^{2} - 64 t + 281 = 0

- 0.5 x^{2} + 15 x = 0

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(x + 8) (x + 5) = 0