1/2+1/2x²+1/2x 怎么变成5/8-1/2（x-1/2)²

1/2(x^2+x+1)=1/2(x^2+x+1/4+3/4)=1/2(x+1/2)^2 + 3/8.
5/8-1/2(x-1/2)^2 =5/8 - 1/2(x^2-x+1/4)=5/8 -x^2/2 + x/2 - 1/8 = 1/2 - x^2/2 + x/2.
1/2-x^2/2 + x/2 = 1/2(1-x^2+x)=-1/2(x^2-x-1)=-1/2(x^2-x+1/4-5/4)
=-1/2(x-1/2)^2 + 5/8
=5/8 -1/2(x-1/2)^2你是把1拆成了5/4减1/4么，为什么要这样拆，若在不知答案的情况下?是把1拆成5/4-1/4.是为了配方. x^2-x=x^2 - 2*x*(1/2) = x^2 - 2*x*(1/2) + 1/4 - 1/4 = (x-1/2)^2 - 1/4.配方是什么意思?能用完全平方，十字相乘，平方差之类的解决么配方就是将x^2 + ax + b写成完全平方+常数的形式.x^2 + ax + b = x^2 + 2*x*(a/2) + (a/2)^2 + b - (a/2)^2=[x+a/2]^2 + [b-(a/2)^2]前一项,[x+a/2]^2就是完全平方.后一项,[b-(a/2)^2]就是常数哈.