Answer:
b = 2
Step-by-step explanation by completing the square:
Solve for b over the real numbers:
b^2 - 4 b + 4 = 0
Write the left hand side as a square:
(b - 2)^2 = 0
Take the square root of both sides:
b - 2 = 0
Add 2 to both sides:
Answer: b = 2
I'm going to use x in place of b. The reason why is because 'b' shows up in the quadratic formula, so there might be some confusion.
So we want to solve x^2 - 4x + 4 = 0 for x
Note how this equation is the same as 1x^2 - 4x + 4 = 0 and it is in the format ax^2 + bx + c = 0
We see that a = 1, b = -4 and c = 4
We will plug these values into the discriminant formula
d = b^2 - 4ac
d = (-4)^2 - 4(1)(4)
d = 16 - 16
d = 0
The discriminant is 0, so the square root of this is also 0. A discriminant of 0 means that there is only one real solution.
It turns out that the solution is equal to x = -b/(2*a) = -(-4)/(2*1) = 4/2 = 2
If the discriminant were nonzero, then the quadratic formula would be a bit messier.
It might be better to factor. Doing so gets you (x-2)^2 = 0 which becomes x-2 = 0 and x = 2
