Answer:
2.25
Step-by-step explanation:
The number to add is the square of half the x-coefficient:
(3/2)^2 = 9/4 = 2.25
Then you have ...
x^2 +3x +2.25 = 8.25
(x +1.5)^2 = 8.25 . . . . left side shown as a square
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The solution is found by taking the square root.
x +1.5 = ±√8.25
x = -1.5 ±√8.25 . . . . subtract 1.5
x ≈ {-4.3723, 1.3723}
