SOLUTION: Solve by applying the Quadratic Formula. Show your work.thanks p^2 + 3p - 9 = 0

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Question 248228: Solve by applying the Quadratic Formula. Show your work.thanks
p^2 + 3p - 9 = 0
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
p^2 + 3p - 9 = 0
what is the quadratic formula?
the quadratic equation is ax^2+bx+c=0
in your equation a=1; b=3 and c=-9
we solve for x to get the quadratic formula
It is wise to calculate the discriminant (b^2-4ac) first. You have to do it anyways.
It will tell you about the solutions.
It says that your equation can be factored but that is not normal factoring
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-9+=+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=%283%29%5E2-4%2A1%2A-9=45.

Discriminant d=45 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+45+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+45+%29%29%2F2%5C1+=+1.85410196624968
x%5B2%5D+=+%28-%283%29-sqrt%28+45+%29%29%2F2%5C1+=+-4.85410196624968

Quadratic expression 1x%5E2%2B3x%2B-9 can be factored:
1x%5E2%2B3x%2B-9+=+1%28x-1.85410196624968%29%2A%28x--4.85410196624968%29
Again, the answer is: 1.85410196624968, -4.85410196624968. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-9+%29


What other way can we solve this equation?
complete the square
p^2 + 3p - 9 = 0
p^2+3p=9=36/4
add (3/2)^2 to both sides
p^2+3p+9/4=(36+9)/4
p^2+3p+9/4=(45)/4
factor
(p+3/2)^2=(3sqrt(5)/2)^2
p+3/2=+\-(3sqrt)5//2
subtract 3/2 from both sides
p=-3/2+3sqrt(5)/2
p=-3/2-3sqrt(5)/2
factor out 3/2