Solve the Following Quadratic Equation by Factorization
Question:
\[ x^2-x-a(a+1)=0 \]Solution
Given,
\[ x^2-x-a(a+1)=0 \]Rewrite the constant term:
\[ x^2-x-a^2-a=0 \]Splitting the middle term:
\[ x^2+ax-(a+1)x-a(a+1)=0 \]Taking common factors:
\[ x(x+a)-(a+1)(x+a)=0 \] \[ (x+a)(x-a-1)=0 \]Therefore,
\[ x+a=0 \] or \[ x-a-1=0 \] \[ x=-a \] or \[ x=a+1 \]