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受欢迎的代数 >

(x^2-4x+4)-((20x+8)^2)/(225)=4

解答

(x^{2} - 4 x + 4) - \frac{( 20 x + 8 ) ^{2}}{225} = 4

解答

x = - \frac{2 ( 61 + 3 401 )}{35}, x = - \frac{2 ( 61 - 3 401 )}{35}

+1

十进制

x = - 6.91856 \dots, x = - 0.05285 \dots

求解步骤

(x^{2} - 4 x + 4) - \frac{( 20 x + 8 ) ^{2}}{225} = 4

在两边乘以

225

225 (x^{2} - 4 x + 4) - (20 x + 8)^{2} = 900

展开

225 (x^{2} - 4 x + 4) - (20 x + 8)^{2} : - 175 x^{2} - 1220 x + 836

- 175 x^{2} - 1220 x + 836 = 900

将

900

para o lado esquerdo

- 175 x^{2} - 1220 x - 64 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 1220 ) \pm ( - 1220 ) ^{2} - 4 ( - 175 ) ( - 64 )}{2 ( - 175 )}

(- 1220)^{2} - 4 (- 175) (- 64) = 60401

x_{1, 2} = \frac{- ( - 1220 ) \pm 60 401}{2 ( - 175 )}

将解分隔开

x_{1} = \frac{- ( - 1220 ) + 60 401}{2 ( - 175 )}, x_{2} = \frac{- ( - 1220 ) - 60 401}{2 ( - 175 )}

x = \frac{- ( - 1220 ) + 60 401}{2 ( - 175 )} : - \frac{2 ( 61 + 3 401 )}{35}

x = \frac{- ( - 1220 ) - 60 401}{2 ( - 175 )} : - \frac{2 ( 61 - 3 401 )}{35}

二次方程组的解是:

x = - \frac{2 ( 61 + 3 401 )}{35}, x = - \frac{2 ( 61 - 3 401 )}{35}

作图

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