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受欢迎的代数 >

(2x-3)^2=(x-5)^2+(2x+3)(2x-7)

解答

(2 x - 3)^{2} = (x - 5)^{2} + (2 x + 3) (2 x - 7)

解答

x = 3 - 14, x = 3 + 14

+1

十进制

x = - 0.74165 \dots, x = 6.74165 \dots

求解步骤

(2 x - 3)^{2} = (x - 5)^{2} + (2 x + 3) (2 x - 7)

展开

(2 x - 3)^{2} : 4 x^{2} - 12 x + 9

展开

(x - 5)^{2} + (2 x + 3) (2 x - 7) : 5 x^{2} - 18 x + 4

4 x^{2} - 12 x + 9 = 5 x^{2} - 18 x + 4

将

4

para o lado esquerdo

4 x^{2} - 12 x + 5 = 5 x^{2} - 18 x

将

18 x

para o lado esquerdo

4 x^{2} + 6 x + 5 = 5 x^{2}

将

5 x^{2}

para o lado esquerdo

- x^{2} + 6 x + 5 = 0

使用求根公式求解

x_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 ( - 1 ) \cdot 5}{2 ( - 1 )}

6^{2} - 4 (- 1) \cdot 5 = 214

x_{1, 2} = \frac{- 6 \pm 2 14}{2 ( - 1 )}

将解分隔开

x_{1} = \frac{- 6 + 2 14}{2 ( - 1 )}, x_{2} = \frac{- 6 - 2 14}{2 ( - 1 )}

x = \frac{- 6 + 2 14}{2 ( - 1 )} : 3 - 14

x = \frac{- 6 - 2 14}{2 ( - 1 )} : 3 + 14

二次方程组的解是:

x = 3 - 14, x = 3 + 14

作图

流行的例子

x^{2} = 5^{2} + 5^{2}

solvefor y,(x-h)^2+(y-k)^2=r^2

so l v e f or y, (x - h)^{2} + (y - k)^{2} = r^{2}

5 (c + 1)^{2} = 25

9 x + 5 = 4 (x^{2} - 1)

solvefor x,x^2+14xy+49y^2=100

so l v e f or x, x^{2} + 14 x y + 49 y^{2} = 100