why must we complete square in order to solve a quadratic equation?
i know how the quadratic formula derived, but in order to get that formula, we have to complete the square. why? how did they know that completeing the square would give the right formula?
i hope u got what i mean*-*
thanks
2006-09-23 11:47:13 · 6 answers · asked by Ganbatteru 3 in Science & Mathematics ➔ Mathematics
You have an x^2 in your equation, but you want an answer in the form of x=.... So what you might try is to isolate the x^2 on the left side, and have evereything else on the right side, and then take the square root of both sides. The problem with this is than you have x's on the left side under the square root sign, so you can't isolate all the x's on one side. The clever trick is to have all the x's on one side, and complete the square, so that when you take the square root of both sides, you can then isolate (ie. solve for) x. Now you have x=.... with no x's mixed in with the right hand side. So the reason you have to complete the square is to get all the x's on one side and still be able to take the square root.
2006-09-23 12:06:36 · answer #1 · answered by WildOtter 5 · 1⤊ 0⤋
A quadratic equation ax^2+bx+c=0 has no obvious solution
just looking at it, the way a linear equation ax+b=c does.
But even a linear equation takes solving to get x = -c/a + b/a.
Way back when they were first studied, some brilliant person
trying to solve for the zeros of a parabola figured out that there
must be exactly two such solutions (except in the degenerate
cases). Factoring doesn't always work.
So experimentation led to the completing the square method.
This is how we derive the general solution formula, which we
can then use any time to solve any quadratic equation.
2006-09-23 11:58:41 · answer #2 · answered by David Y 5 · 0⤊ 0⤋
Yes, I understand your question perfectly.
There are many ways to solve a quadratic equation, but the general formula is demonstrated this way. If you find another way, you can use it.
You are using this fact:
(a+b)^2 = a^2 + 2ab + b^2
So that you can find a+b, thats why the square root is a part of the formula.
I dont know if this convinces you as an explanation. I will wonder if I can explain this to you in a better way
Ana
2006-09-23 11:58:05 · answer #3 · answered by MathTutor 6 · 0⤊ 1⤋
Because 'completing the square' means that you are creating a polynomial which can be written as
(x ± a)*(x ±b) which has roots of a and b.
Doug
2006-09-23 12:01:25 · answer #4 · answered by doug_donaghue 7 · 0⤊ 0⤋
To know the vertex of parabola, because quadratic equation is always parabola.
2006-09-23 12:52:17 · answer #5 · answered by Amar Soni 7 · 0⤊ 0⤋
x^2 + bx/a + c/a = 0 (dividing by by making use of a) (x + b/2a)^2 = b^2/4a^2 - c/a (polishing off the sq.) x + b/2a = +/- [sqrt(b^2 -4ac)]2a (simplifying and taking squarert both aspect) x = -b/2a +/- [sqrt (b^2 - 4ac)]/2a (rearranging) memorize this derivation in case you intend on being a severe mathematician
2016-11-23 17:57:23 · answer #6 · answered by ? 4 · 0⤊ 0⤋