Step-by-step explanation:
The first step in completing the square is to make the leading coefficient 1.
3 − 4x = 5x² − 14x
First, add 4x to both sides.
3 = 5x² − 10x
Divide both sides by 5.
3/5 = x² − 2x
The next step is to create the square. Take half of -2, square it, then add the result to both sides. (-2/2)² = 1.
3/5 + 1 = x² − 2x + 1
8/5 = x² − 2x + 1
Finally, factor the perfect square and solve for x.
8/5 = (x − 1)²
Take the square root of both sides.
±√(8/5) = x − 1
Add 1 to both sides.
x = 1 ± √(8/5)
