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受欢迎的代数 >

(2x-3)^2+23=(x+5)^2

解答

(2 x - 3)^{2} + 23 = (x + 5)^{2}

解答

x = 7, x = \frac{1}{3}

+1

十进制

x = 7, x = 0.33333 \dots

求解步骤

(2 x - 3)^{2} + 23 = (x + 5)^{2}

展开

(2 x - 3)^{2} + 23 : 4 x^{2} - 12 x + 32

展开

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

4 x^{2} - 12 x + 32 = x^{2} + 10 x + 25

将

25

para o lado esquerdo

4 x^{2} - 12 x + 7 = x^{2} + 10 x

将

10 x

para o lado esquerdo

4 x^{2} - 22 x + 7 = x^{2}

将

x^{2}

para o lado esquerdo

3 x^{2} - 22 x + 7 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 22 ) \pm ( - 22 ) ^{2} - 4 \cdot 3 \cdot 7}{2 \cdot 3}

(- 22)^{2} - 4 \cdot 3 \cdot 7 = 20

x_{1, 2} = \frac{- ( - 22 ) \pm 20}{2 \cdot 3}

将解分隔开

x_{1} = \frac{- ( - 22 ) + 20}{2 \cdot 3}, x_{2} = \frac{- ( - 22 ) - 20}{2 \cdot 3}

x = \frac{- ( - 22 ) + 20}{2 \cdot 3} : 7

x = \frac{- ( - 22 ) - 20}{2 \cdot 3} : \frac{1}{3}

二次方程组的解是:

x = 7, x = \frac{1}{3}

作图

流行的例子

x (x - 3) = 40

r^{2} = 4

4 x^{2} + 15 x - 4 = 0

100x^2+120x+36=0

100 x^{2} + 120 x + 36 = 0

3 x^{2} - 4 x - 8 = - 6