The constant term in a complete square is the square of half the x coefficient.
X^2 + 3x - 5 = 0
x^2 + 3x = 5 (add 5 to both sides)
x^2 + 3x + (3/2)^2 = 5 + (3/2)^2 (complete the square on the left, add the same amount on the right so the equal sign is still true)
(x + 1.5)^2 = 5 + 2.25 (show the square, change to decimal for clarity)
x + 1.5 = ±√7.25 (square root both sides. Note we need ± .)
x = -1.5 ± √7.25 (subtract 1.5 from both sides)
X^2 + 3x - 5 = 0
x^2 + 3x = 5 (add 5 to both sides)
x^2 + 3x + (3/2)^2 = 5 + (3/2)^2 (complete the square on the left, add the same amount on the right so the equal sign is still true)
(x + 1.5)^2 = 5 + 2.25 (show the square, change to decimal for clarity)
x + 1.5 = ±√7.25 (square root both sides. Note we need ± .)
x = -1.5 ± √7.25 (subtract 1.5 from both sides)
