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受欢迎的代数 >

solvefor a,f(a+7)=(a+7)^2+1

解答

求解

a, f (a + 7) = (a + 7)^{2} + 1

解答

a = \frac{- 14 + f + f ^{2} - 4}{2}, a = \frac{- 14 + f - f ^{2} - 4}{2}

求解步骤

f (a + 7) = (a + 7)^{2} + 1

展开

f (a + 7) : a f + 7 f

展开

(a + 7)^{2} + 1 : a^{2} + 14 a + 50

a f + 7 f = a^{2} + 14 a + 50

交换两边

a^{2} + 14 a + 50 = a f + 7 f

将

7 f

para o lado esquerdo

a^{2} + 14 a + 50 - 7 f = a f

将

a f

para o lado esquerdo

a^{2} + 14 a + 50 - 7 f - a f = 0

改写成标准形式

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

a^{2} + (14 - f) a + 50 - 7 f = 0

使用求根公式求解

a_{1, 2} = \frac{- ( 14 - f ) \pm ( 14 - f ) ^{2} - 4 \cdot 1 \cdot ( 50 - 7 f )}{2 \cdot 1}

化简

(14 - f)^{2} - 4 \cdot 1 \cdot (50 - 7 f) : f^{2} - 4

a_{1, 2} = \frac{- ( 14 - f ) \pm f ^{2} - 4}{2 \cdot 1}

将解分隔开

a_{1} = \frac{- ( 14 - f ) + f ^{2} - 4}{2 \cdot 1}, a_{2} = \frac{- ( 14 - f ) - f ^{2} - 4}{2 \cdot 1}

a = \frac{- ( 14 - f ) + f ^{2} - 4}{2 \cdot 1} : \frac{- 14 + f + f ^{2} - 4}{2}

a = \frac{- ( 14 - f ) - f ^{2} - 4}{2 \cdot 1} : \frac{- 14 + f - f ^{2} - 4}{2}

二次方程组的解是:

a = \frac{- 14 + f + f ^{2} - 4}{2}, a = \frac{- 14 + f - f ^{2} - 4}{2}

作图

流行的例子

completesquare 5x^2-10x-75=0

co m pl e t es q u a re 5 x^{2} - 10 x - 75 = 0

s^{2} + 6 s + 36.9 = 0

completesquare-2x^2+3x-1

co m pl e t es q u a re - 2 x^{2} + 3 x - 1

- p^{2} + 2 p + 3 = 0

15+2(2.5-x)=11+x^2

15 + 2 (2.5 - x) = 11 + x^{2}