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受欢迎的代数 >

solvefor x,f(x+3)=4x^2+4x-3

解答

求解

x, f (x + 3) = 4 x^{2} + 4 x - 3

解答

x = \frac{- 4 + f + f ^{2} + 40 f + 64}{8}, x = \frac{- 4 + f - f ^{2} + 40 f + 64}{8}

求解步骤

f (x + 3) = 4 x^{2} + 4 x - 3

展开

f (x + 3) : x f + 3 f

x f + 3 f = 4 x^{2} + 4 x - 3

交换两边

4 x^{2} + 4 x - 3 = x f + 3 f

将

3 f

para o lado esquerdo

4 x^{2} + 4 x - 3 - 3 f = x f

将

x f

para o lado esquerdo

4 x^{2} + 4 x - 3 - 3 f - x f = 0

改写成标准形式

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

4 x^{2} + (4 - f) x - 3 - 3 f = 0

使用求根公式求解

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

化简

(4 - f)^{2} - 4 \cdot 4 (- 3 - 3 f) : f^{2} + 40 f + 64

x_{1, 2} = \frac{- ( 4 - f ) \pm f ^{2} + 40 f + 64}{2 \cdot 4}

将解分隔开

x_{1} = \frac{- ( 4 - f ) + f ^{2} + 40 f + 64}{2 \cdot 4}, x_{2} = \frac{- ( 4 - f ) - f ^{2} + 40 f + 64}{2 \cdot 4}

x = \frac{- ( 4 - f ) + f ^{2} + 40 f + 64}{2 \cdot 4} : \frac{- 4 + f + f ^{2} + 40 f + 64}{8}

x = \frac{- ( 4 - f ) - f ^{2} + 40 f + 64}{2 \cdot 4} : \frac{- 4 + f - f ^{2} + 40 f + 64}{8}

二次方程组的解是:

x = \frac{- 4 + f + f ^{2} + 40 f + 64}{8}, x = \frac{- 4 + f - f ^{2} + 40 f + 64}{8}

作图

流行的例子

x^2+2x-48=(x+8)

x^{2} + 2 x - 48 = (x + 8)

0 = 30 - 4.9 x^{2}

(y - 2)^{2} = 9

8 (x - 19)^{2} = 0

3 x^{2} = 2 x^{2}