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
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
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
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