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受欢迎的代数 >

(1/2 x+3)^2-x(2x-1)=-1

解答

(\frac{1}{2} x + 3)^{2} - x (2 x - 1) = - 1

解答

x = - \frac{2 ( - 4 + 86 )}{7}, x = \frac{2 ( 4 + 86 )}{7}

+1

十进制

x = - 1.50674 \dots, x = 3.79246 \dots

求解步骤

(\frac{1}{2} x + 3)^{2} - x (2 x - 1) = - 1

展开

(\frac{1}{2} x + 3)^{2} - x (2 x - 1) : - \frac{7}{4} x^{2} + 4 x + 9

- \frac{7}{4} x^{2} + 4 x + 9 = - 1

将

1

para o lado esquerdo

- \frac{7}{4} x^{2} + 4 x + 10 = 0

改写成标准形式

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

- \frac{7 x ^{2}}{4} + 4 x + 10 = 0

使用求根公式求解

x_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 ( - \frac{7}{4} ) \cdot 10}{2 ( - \frac{7}{4} )}

4^{2} - 4 (- \frac{7}{4}) \cdot 10 = 86

x_{1, 2} = \frac{- 4 \pm 86}{2 ( - \frac{7}{4} )}

将解分隔开

x_{1} = \frac{- 4 + 86}{2 ( - \frac{7}{4} )}, x_{2} = \frac{- 4 - 86}{2 ( - \frac{7}{4} )}

x = \frac{- 4 + 86}{2 ( - \frac{7}{4} )} : - \frac{2 ( - 4 + 86 )}{7}

x = \frac{- 4 - 86}{2 ( - \frac{7}{4} )} : \frac{2 ( 4 + 86 )}{7}

二次方程组的解是:

x = - \frac{2 ( - 4 + 86 )}{7}, x = \frac{2 ( 4 + 86 )}{7}

作图

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