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受欢迎的代数 >

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

解答

求解

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

解答

x = \frac{- 2 + f + f ^{2} + 44 f + 52}{8}, x = \frac{- 2 + f - f ^{2} + 44 f + 52}{8}

求解步骤

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

展开

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

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

交换两边

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

将

3 f

para o lado esquerdo

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

将

x f

para o lado esquerdo

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

改写成标准形式

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

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

使用求根公式求解

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

化简

(2 - f)^{2} - 4 \cdot 4 (- 3 - 3 f) : f^{2} + 44 f + 52

x_{1, 2} = \frac{- ( 2 - f ) \pm f ^{2} + 44 f + 52}{2 \cdot 4}

将解分隔开

x_{1} = \frac{- ( 2 - f ) + f ^{2} + 44 f + 52}{2 \cdot 4}, x_{2} = \frac{- ( 2 - f ) - f ^{2} + 44 f + 52}{2 \cdot 4}

x = \frac{- ( 2 - f ) + f ^{2} + 44 f + 52}{2 \cdot 4} : \frac{- 2 + f + f ^{2} + 44 f + 52}{8}

x = \frac{- ( 2 - f ) - f ^{2} + 44 f + 52}{2 \cdot 4} : \frac{- 2 + f - f ^{2} + 44 f + 52}{8}

二次方程组的解是:

x = \frac{- 2 + f + f ^{2} + 44 f + 52}{8}, x = \frac{- 2 + f - f ^{2} + 44 f + 52}{8}

作图

流行的例子

completesquare x^2-x-4

co m pl e t es q u a re x^{2} - x - 4

(x - 4)^{2} - 3 = 6

(w + 1)^{2} - 32 = 0

(x - 4)^{2} - 2 = 0

b^{2} = 0