Answer
Zero-Factor Property
Work Step by Step
In the form $ax^2+bx+c=0,$ the given equation, $
4x^2-3x=1
,$ is equivalent to
\begin{align*}
4x^2-3x-1=0
.\end{align*}
Using the discriminant of a quadratic equation, which is given by $b^2-4ac,$ then
\begin{align*}
b^2-4ac&=
(-3)^2-4(4)(-1)
\\&=
9+16
\\&=
25
\\&=
5^2
.\end{align*}
Since the discriminant is zero, and all the coefficients of the given equation are integers, then the given equation can be factored. The factors can then be equated to zero. Hence, the Zero-Factor Property is the most appropriate way to solve the given equation.