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 ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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!       Log On


   

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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-4=20.

Discriminant d=20 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+20+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+20+%29%29%2F2%5C1+=+3.23606797749979
x%5B2%5D+=+%28-%28-2%29-sqrt%28+20+%29%29%2F2%5C1+=+-1.23606797749979

Quadratic expression 1x%5E2%2B-2x%2B-4 can be factored:
1x%5E2%2B-2x%2B-4+=+%28x-3.23606797749979%29%2A%28x--1.23606797749979%29
Again, the answer is: 3.23606797749979, -1.23606797749979. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-4+%29

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-x-2=x%2B2
x%5E2-2x-4=0
%28x%2B__%29%28x-__%29......since you have -2x-4, you can't complete the square like this %28x%2B__%29%28x-__%29
so, to find solutions, use quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%2A1%29+
x+=+%282+%2B-+sqrt%28+4%2B16+%29%29%2F2+
x+=+%282+%2B-+sqrt%28+20+%29%29%2F2+
x+=+%282+%2B-+sqrt%28+4%2A5+%29%29%2F2+
x+=+%282+%2B-+2sqrt%28+5%29%29%2F2+....simplify
x+=1+%2B-+sqrt%28+5%29+
solutions:
x+=1+%2Bsqrt%28+5%29+ => x+=1+%2B2.24+ => x=3.24
x+=1-sqrt%28+5%29+ => x+=1+-2.24+ => x=-1.24

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B2%2C+x%5E2-x-2%29+






Answer by KMST(5328) About Me  (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 x%5E2-2x is part of x%5E2-2x%2B1=%28x-1%29%5E2
So I would do this:
x%5E2-2x-4=0
x%5E2-2x=4
x%5E2-2x%2B1=4%2B1 (I added 1 to complete the square on the side of the equal sign)
x-1%29%5E2=5
The two solutions come from the two possible values for x-1:
x-1=sqrt%285%29-->x=1%2Bsqrt%285%29
x-1=-sqrt%285%29-->x=1-sqrt%285%29
We can write them both in one as
highlight%28x=1+%2B-+sqrt%285%29%29
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.