Answer: To complete the square for the quadratic equation x^2 + 5x - 1 = 0, we need to add a constant term that will allow us to rewrite the left-hand side of the equation as a perfect square trinomial.
To determine this constant term, we take half of the coefficient of x, square it, and add it to both sides of the equation. The coefficient of x in this equation is 5, so we have:
(5/2)^2 = 6.25
Adding 6.25 to both sides of the equation, we get:
x^2 + 5x - 1 + 6.25 = 6.25
x^2 + 5x + 5.25 = 0
Now, we can factor this equation as:
(x + 2.5)^2 = 0.25
To solve for x, we take the square root of both sides and solve for x:
x + 2.5 = ±0.5
x = -2.5 ± 0.5
So, the number that had to be added to "complete the square" was 6.25.
Explanation: