Chapter 9 - Solving Quadratic Equations - 9.5 - Solving Quadratic Equations Using the Quadratic Formula - Monitoring Progress - Page 516: 4

$x=\frac{1}{2}$

$4x^{2}-4x=-1\implies 4x^{2}-4x+1=0$ Comparing $4x^{2}-4x+1=0$ with $ax^{2}+bx+c=0$, we get $a=4$, $b=-4$ and $c=1$. The quadratic formula is $x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Substituting the values, we get $x=\frac{-(-4) \pm \sqrt {(-4)^{2}-4(4)(1)}}{(2)(4)}=\frac{4 }{8}=\frac{1}{2}$