SOLUTION: Please help me with this.I have a project that is 4 parts. I'm not sure how to do this part. I have to do a quadratic formula for x^2 + 6x = 16 I have to a. put it in standar

Algebra ->  Rational-functions -> SOLUTION: Please help me with this.I have a project that is 4 parts. I'm not sure how to do this part. I have to do a quadratic formula for x^2 + 6x = 16 I have to a. put it in standar      Log On


   

Question 529624: Please help me with this.I have a project that is 4 parts. I'm not sure how to do this part. I have to do a quadratic formula for x^2 + 6x = 16
I have to
a. put it in standard form
b. state the values of a,b,and c
c. state the quadratic formula
d. show the substitution step
e. show step by step the evaluation of the work until Ireach a solution.
This is very important and I don't want to get it wrong, so I need your help!
thank you so much!


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + 6x = 16
I have to
a. put it in standard form
x%5E2+%2B+6x+-+16+=+0
Or do you mean f%28x%29+=+%28x%2B3%29%5E2+-+25 ?
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b. state the values of a,b,and c
a = 1
b = 6
c = -16
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c. state the quadratic formula
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B-16+=+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=%286%29%5E2-4%2A1%2A-16=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+2
x%5B2%5D+=+%28-%286%29-sqrt%28+100+%29%29%2F2%5C1+=+-8

Quadratic expression 1x%5E2%2B6x%2B-16 can be factored:
1x%5E2%2B6x%2B-16+=+%28x-2%29%2A%28x--8%29
Again, the answer is: 2, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-16+%29

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d. show the substitution step
don't know what that means.
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e. show step by step the evaluation of the work until Ireach a solution.
See above.