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受欢迎的代数 >

2x^2+1=(x+5)^2

解答

2 x^{2} + 1 = (x + 5)^{2}

解答

x = - 2, x = 12

求解步骤

2 x^{2} + 1 = (x + 5)^{2}

展开

(x + 5)^{2} : x^{2} + 10 x + 25

2 x^{2} + 1 = x^{2} + 10 x + 25

交换两边

x^{2} + 10 x + 25 = 2 x^{2} + 1

将

1

para o lado esquerdo

x^{2} + 10 x + 24 = 2 x^{2}

将

2 x^{2}

para o lado esquerdo

- x^{2} + 10 x + 24 = 0

使用求根公式求解

x_{1, 2} = \frac{- 10 \pm 1 0 ^{2} - 4 ( - 1 ) \cdot 24}{2 ( - 1 )}

1 0^{2} - 4 (- 1) \cdot 24 = 14

x_{1, 2} = \frac{- 10 \pm 14}{2 ( - 1 )}

将解分隔开

x_{1} = \frac{- 10 + 14}{2 ( - 1 )}, x_{2} = \frac{- 10 - 14}{2 ( - 1 )}

x = \frac{- 10 + 14}{2 ( - 1 )} : - 2

x = \frac{- 10 - 14}{2 ( - 1 )} : 12

二次方程组的解是:

x = - 2, x = 12

作图

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