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受欢迎的代数 >

(1/2 x+7)^2+7(1/2 x+7)+12=0

解答

(\frac{1}{2} x + 7)^{2} + 7 (\frac{1}{2} x + 7) + 12 = 0

解答

x = - 20, x = - 22

求解步骤

(\frac{1}{2} x + 7)^{2} + 7 (\frac{1}{2} x + 7) + 12 = 0

展开

(\frac{1}{2} x + 7)^{2} + 7 (\frac{1}{2} x + 7) + 12 : \frac{1}{4} x^{2} + \frac{21}{2} x + 110

\frac{1}{4} x^{2} + \frac{21}{2} x + 110 = 0

改写成标准形式

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

\frac{x ^{2}}{4} + \frac{21 x}{2} + 110 = 0

使用求根公式求解

x_{1, 2} = \frac{- \frac{21}{2} \pm ( \frac{21}{2} ) ^{2} - 4 \cdot \frac{1}{4} \cdot 110}{2 \cdot \frac{1}{4}}

(\frac{21}{2})^{2} - 4 \cdot \frac{1}{4} \cdot 110 = \frac{1}{2}

x_{1, 2} = \frac{- \frac{21}{2} \pm \frac{1}{2}}{2 \cdot \frac{1}{4}}

将解分隔开

x_{1} = \frac{- \frac{21}{2} + \frac{1}{2}}{2 \cdot \frac{1}{4}}, x_{2} = \frac{- \frac{21}{2} - \frac{1}{2}}{2 \cdot \frac{1}{4}}

x = \frac{- \frac{21}{2} + \frac{1}{2}}{2 \frac{1}{4}} : - 20

x = \frac{- \frac{21}{2} - \frac{1}{2}}{2 \frac{1}{4}} : - 22

二次方程组的解是:

x = - 20, x = - 22

作图

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