Multiply both sides by \(2x\).
\[2{x}^{2}+2=5x\]
Move all terms to one side.
\[2{x}^{2}+2-5x=0\]
Split the second term in \(2{x}^{2}+2-5x\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[2\times 2=4\]
Ask: Which two numbers add up to \(-5\) and multiply to \(4\)?
Split \(-5x\) as the sum of \(-x\) and \(-4x\).
\[2{x}^{2}-x-4x+2\]
\[2{x}^{2}-x-4x+2=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[x(2x-1)-2(2x-1)=0\]
Factor out the common term \(2x-1\).
\[(2x-1)(x-2)=0\]
Solve for \(x\).
Ask: When will \((2x-1)(x-2)\) equal zero?
When \(2x-1=0\) or \(x-2=0\)
Solve each of the 2 equations above.
\[x=\frac{1}{2},2\]
\[x=\frac{1}{2},2\]
Decimal Form: 0.5, 2
x=1/2,2
