Let f(x)=x^2+4x. Which equation among the following is the correct result after setting f(x) equal to 0

and completing the square?

2 answers

To complete the square for f(x) = x^2 + 4x, we add and subtract the square of half the coefficient of x, which is (4/2)^2 = 4, inside the parenthesis:

f(x) = x^2 + 4x
f(x) + 4 = x^2 + 4x + 4
f(x) + 4 = (x + 2)^2

Now we can set f(x) + 4 equal to 0 to find the solution:

f(x) + 4 = 0
(x + 2)^2 = 0

Taking the square root of both sides, we get:

x + 2 = 0

So the equation obtained after completing the square and setting f(x) equal to 0 is:

(x + 2)^2 = 0
You want
x^2+4x = 0
by completing the square:
x^2 + 4x + 4 = 4
(x+2)^2 = 4
x + 2 = ± 2
x = 0 or x = -4

we could get the same result by
x^2 + 4x = 0
x(x+4) = 0
x = 0 or x = -4