Complete the square for the problem x^2 + 16x + 63
To complete the square for the quadratic equation x^2 + 16x + 63, we need to find a value "c" such that when we add and subtract it within the equation, we create a perfect square trinomial.
The formula to complete the square for a quadratic equation in the form of ax^2 + bx + c is:
(ax^2 + bx + c) + (c) = (x + (b/2))^2
In our case, the equation is x^2 + 16x + 63.
To find the value of "c" that completes the square:
b = 16
c = (b/2)^2 = (16/2)^2 = 64
So, the complete square will be x^2 + 16x + 64 = (x + 8)^2
But in the given equation, there is an extra 63 that needs to be accounted for.
x^2 + 16x + 63 = (x + 8)^2 - 1
Therefore, the completed square form of x^2 + 16x + 63 is (x + 8)^2 - 1.