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受欢迎的代数 >

solvefor x,f(x+2-2)=2(x+2)^2-3(x+2)-1

解答

求解

x, f (x + 2 - 2) = 2 (x + 2)^{2} - 3 (x + 2) - 1

解答

x = \frac{- 5 + f + f ^{2} - 10 f + 17}{4}, x = \frac{- 5 + f - f ^{2} - 10 f + 17}{4}

求解步骤

f (x + 2 - 2) = 2 (x + 2)^{2} - 3 (x + 2) - 1

展开

f (x + 2 - 2) : x f

展开

2 (x + 2)^{2} - 3 (x + 2) - 1 : 2 x^{2} + 5 x + 1

x f = 2 x^{2} + 5 x + 1

交换两边

2 x^{2} + 5 x + 1 = x f

将

x f

para o lado esquerdo

2 x^{2} + 5 x + 1 - x f = 0

改写成标准形式

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

2 x^{2} + (5 - f) x + 1 = 0

使用求根公式求解

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

化简

(5 - f)^{2} - 4 \cdot 2 \cdot 1 : f^{2} - 10 f + 17

x_{1, 2} = \frac{- ( 5 - f ) \pm f ^{2} - 10 f + 17}{2 \cdot 2}

将解分隔开

x_{1} = \frac{- ( 5 - f ) + f ^{2} - 10 f + 17}{2 \cdot 2}, x_{2} = \frac{- ( 5 - f ) - f ^{2} - 10 f + 17}{2 \cdot 2}

x = \frac{- ( 5 - f ) + f ^{2} - 10 f + 17}{2 \cdot 2} : \frac{- 5 + f + f ^{2} - 10 f + 17}{4}

x = \frac{- ( 5 - f ) - f ^{2} - 10 f + 17}{2 \cdot 2} : \frac{- 5 + f - f ^{2} - 10 f + 17}{4}

二次方程组的解是:

x = \frac{- 5 + f + f ^{2} - 10 f + 17}{4}, x = \frac{- 5 + f - f ^{2} - 10 f + 17}{4}

作图

流行的例子

1 5^{2} + 8^{2} = r^{2}

0.2 x^{2} + x - 140 = 0

2 x^{2} - 33 = 39

0.1 x^{2} + x - 100 = 0

- 8 r^{2} = - 512