Appendix A - Equations and Inequalities - Page 417: 41

{$\frac{1}{2}$}

$4x^{2}-4x+1=0$ $4x^{2}-2x-2x+1=0$ $2x(2x-1)-1(2x-1)=0$ $(2x-1)(2x-1)=0$ $(2x-1)=0$ or $(2x-1)=0$ $x=\frac{1}{2}$ or $x=\frac{1}{2}$ Check: Substituting $x=\frac{1}{2}$ in the equation, $4(\frac{1}{2})^{2}-4(\frac{1}{2})+1=0$ $\frac{4}{4}-\frac{4}{2}+1=0$ $1-2+1=0$ $0=0$ The value checks and the solution set is {$\frac{1}{2}$}