SOLUTION: If I have the quadratic function, f(x)= (x^2)-x-12, and I want to find the x-intercept, I have to set y = 0, and factor like so: 0 = (x-4)(x+3). The questions is: why can't I co

Question 1009738: If I have the quadratic function, f(x)= (x^2)-x-12, and I want to find the x-intercept, I have to set y = 0, and factor like so: 0 = (x-4)(x+3).
The questions is: why can't I complete the square or factor like so: 0 = x(x-1)-12 (which leads to 0 = (x-1)(x-12))? Doing either of those alternative techniques results in different x-intercepts.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You're not doing the algebra right. Completing
the square should work, though.

Take the square root of both sides
(1)
and, also:
(2)
-------------------
(1)
(1)
and
(2)
(2)
------------------
So, the factors are:

You could also use the quadratic formula
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

If I have the quadratic function, f(x)= (x^2)-x-12, and I want to find the x-intercept, I have to set y = 0, and factor like so: 0 = (x-4)(x+3).
The questions is: why can't I complete the square or factor like so: 0 = x(x-1)-12 (which leads to 0 = (x-1)(x-12))? Doing either of those alternative techniques results in different x-intercepts.

You can use the "complete the square" method to solve for the x-intercepts/solutions to the equation/roots.
However, factoring CANNOT be done the following way you proposed:

From this, you CANNOT obtain x - 1 and x - 12 as factors. That's not the proper way to factor a trinomial in
order to find its roots. The 1^st method: , though is indeed correct.
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