Split the second term in \(2{x}^{2}-3x+1\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[2\times 1=2\]
Ask: Which two numbers add up to \(-3\) and multiply to \(2\)?
Split \(-3x\) as the sum of \(-x\) and \(-2x\).
\[2{x}^{2}-x-2x+1\]
\[2{x}^{2}-x-2x+1=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[x(2x-1)-(2x-1)=0\]
Factor out the common term \(2x-1\).
\[(2x-1)(x-1)=0\]
Solve for \(x\).
Ask: When will \((2x-1)(x-1)\) equal zero?
When \(2x-1=0\) or \(x-1=0\)
Solve each of the 2 equations above.
\[x=\frac{1}{2},1\]
\[x=\frac{1}{2},1\]
Decimal Form: 0.5, 1
x=1/2,1
