SOLUTION: I need to solve this, I was given two initial equations y=x^2-x-2 and y=x+2 here's how far I got x^2-x-2=x+2 x^2-2x-4=0 (x+__)(x-__) HELP thanks!

Algebra.Com
Question 785528: I need to solve this, I was given two initial equations y=x^2-x-2 and y=x+2
here's how far I got
x^2-x-2=x+2
x^2-2x-4=0
(x+__)(x-__)
HELP
thanks!
Found 3 solutions by xinxin, MathLover1, KMST:
Answer by xinxin(76)   (Show Source): You can put this solution on YOUR website!
Do not use factoring to do this one; it will make the problem harder.
The best way of doing this is to use quadratic formula.(As you would see the factoring expression is listed in the solution)
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=20 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3.23606797749979, -1.23606797749979. Here's your graph:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!



......since you have , you can't complete the square like this
so, to find solutions, use quadratic formula:





....simplify

solutions:
=> =>
=> =>








Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
Factoring is a very efficient method to solve some quadratic equations.
However, sometimes it does not work.
Not every quadratic equation can be solved by factoring.
The numbers to fill in those blanks could be found by other means, but they may be irrational numbers or numbers that are not real numbers (which you may not have studied yet).
There are two sure ways to solve a quadratic equation.
One is "completing the square" using your brain.
The other is applying a memorized formula called the quadratic formula.
Sometimes, it is easier to use the quadratic formula, but in this case, both approaches work well.

COMPLETING THE SQUARE:
For this particular equation, completing the square would be my choice.
It is easy to see that is part of
So I would do this:


(I added 1 to complete the square on the side of the equal sign)

The two solutions come from the two possible values for :
-->
-->
We can write them both in one as

If the coefficients in the equation were more cumbersome (as it often happens in real life problems), I would use the quadratic formula, and probably would have some program to do that solve and verify the solution automatically.
RELATED QUESTIONS

I need to solve this equation: 10/(x^2-2x)+4/x=5/(x-2) so far I have 4x+2/(x^2-2x) =... (answered by mananth)
Hi I need to solve and check the equations for x: x/x-2-x+1/x=8/x^2-2x {{{x/(x -... (answered by scianci)
how would I solve the following nonlinear system of equations? {{{yx^2=32}}}... (answered by Edwin McCravy)
I am trying to help my granddaughter and need to explane this to her. x + 4 = y -2 (answered by checkley71)
I was wondering have do you solve this system using elimination x+y=2 x-y=4 I have tryed (answered by Alan3354)
I have the problem almost complete but I can get this, Here is the problem: 2/x - 1 (answered by gypsy1274)
I need help on steps for solving a system of equations in substitution,elimination,and... (answered by MathLover1)
Graph y is greater than or equal to -2x^2+2x+4. I got as far as: x=-b/2a-2/2(-2) I need (answered by ankor@dixie-net.com)
composition of functions Given: f(x)= 2/x (fof)(x) so far i have... (answered by Fombitz)