Can every quadratic be solved by using the completing the square method?
Can every quadratic be solved by using the completing the square method? Yes, it sure seems so.....but, I wouldn't want to do it that way every time!!
Certainly, every quadratic can be solved by the quadratic formula, but I also wouldn't want to use it every time either.
I think you should develop some strategies for which method is best in which circumstances. Purple Math link
There are even websites that will solve the problems for you: Solver
For completing the square, I look for two things: "1" as the lead coefficient (on the
Step 2: take half of the "4", and square that number.
Step 3: Add that number to both sides
Step 4: Factor the trinomial:
Step 5: Take the square root of both sides:
Phew, that's a lot of steps! And it definitely takes practice. One more example:
so, x = 9 or -1. Wow!
Of course, those nice, rational answers tell me that the original problem could have been solved by factoring: (x-9)(x+1)=0
Use the zero product property to solve x = 9 or x = -1.