SOLUTION: Solve the following quadratic equations by factoring or by any of the techniques of this chapter.Share why you chose one method over the other for each problem. {{{4x^2-8x=3=5}}}

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve the following quadratic equations by factoring or by any of the techniques of this chapter.Share why you chose one method over the other for each problem. {{{4x^2-8x=3=5}}}       Log On


   

Question 74861This question is from textbook Beginning Algebra
: Solve the following quadratic equations by factoring or by any of the techniques of this chapter.Share why you chose one method over the other for each problem.
4x%5E2-8x=3=5
The answer I got was 2sqrt%286%2B2%29%2F2,-2sqrt%286%2B2%29%2F2. Is this correct? Thanks. Is this the square root method? Thank. This question is from textbook Beginning Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming the equation looks like this:
4x%5E2-8x%2B3=5
4x%5E2-8x%2B3-5=cross%285-5%29Subtract 5 from both sides
4x%5E2-8x-2=0Plug this into the quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-8x%2B-2+=+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=%28-8%29%5E2-4%2A4%2A-2=96.

Discriminant d=96 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+96+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+96+%29%29%2F2%5C4+=+2.22474487139159
x%5B2%5D+=+%28-%28-8%29-sqrt%28+96+%29%29%2F2%5C4+=+-0.224744871391589

Quadratic expression 4x%5E2%2B-8x%2B-2 can be factored:
4x%5E2%2B-8x%2B-2+=+4%28x-2.22474487139159%29%2A%28x--0.224744871391589%29
Again, the answer is: 2.22474487139159, -0.224744871391589. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-8%2Ax%2B-2+%29

In other words, you should get
x=%288%2Bsqrt%2896%29%29%2F8 and x=%288-sqrt%2896%29%29%2F8
Which reduces to
x=1%2B%28sqrt%286%29%29%2F2 and x=1-%28sqrt%286%29%29%2F2
You were close to the answer, so double check your steps to see where you went wrong.