The square root property seems to be another name for completing the square
x^2 + 5x + 6 = 0
We move the constant to the other side
x^2 + 5x = -6
We square half the linear coefficient and add that to both sides
x^2 + 5x + (5/2)^2 = -6 + 25/4
Now the left side is a perfect square,
(x + 5/2)^2 = 1/4
Here's the square root property part, we take the square root of both sides, remembering the ±
x + 5/2 = ± 1/2
x = -5/2 ± 1/2
Answer: x = -3 or x=-2
We check by plugging in these values to the original equation, and they work.
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x^2 + 6x = 16
Again we add half the linear coefficient, squared, to both sides
x^2 + 6x + 3^2 = 16 + 9
(x + 3)^2 = 25
Here comes the square root property, taking the square root of both sides:
x + 3 = ±5
x = -3 ± 5
x = 2 or x = -8
Again we check by substitution, and they both work
Answer: x = 2 or x = -8