SOLUTION: solve using the quadratic formula this problem is taken from a homework sheet on quadratic equations, can you please show me the necessary steps involed in completing this problem

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Question 64000: solve using the quadratic formula
this problem is taken from a homework sheet on quadratic equations, can you please show me the necessary steps involed in completing this problem.
x^2-3x-3=-5
Found 2 solutions by sarahschober, josmiceli:
Answer by sarahschober(35) About Me  (Show Source):
You can put this solution on YOUR website!
First set the equation equal to zero by adding 5 to both sides.
Then...
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-3x%2B2+=+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=%28-3%29%5E2-4%2A1%2A2=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+2
x%5B2%5D+=+%28-%28-3%29-sqrt%28+1+%29%29%2F2%5C1+=+1

Quadratic expression 1x%5E2%2B-3x%2B2 can be factored:
1x%5E2%2B-3x%2B2+=+%28x-2%29%2A%28x-1%29
Again, the answer is: 2, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B2+%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+3x+-+3+=+-5
You want to get this in the form ax%5E2+%2B+bx+%2B+c+=+0
x%5E2+-+3x+%2B+2+=+0
a = 1
b = -3
c = 2
The quadratic formula is
x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2+-+4%2A1%2A2+%29%29%2F%282%2A1%29+
x+=+%283+%2B-+sqrt%28+9+-+8+%29%29%2F+2+
note that %2B+sqrt%281%29+=+%2B1 and -+sqrt%281%29+=+-1
x+=+%283+%2B+1%29+%2F+2
x+=+2
and
x+=+%283+-+1%29+%2F+2
x+=+1
The roots are x = 2 and x = 1