Question

What number should be added to both sides of the equation to complete the square x^2+3x=6

Answer 1

2.25

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}