SOLUTION: Can someone help me solve these and show all work. I am trying to learn algebra but not doing very good I don't think. I confuse myself more than anything. I can usually get the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can someone help me solve these and show all work. I am trying to learn algebra but not doing very good I don't think. I confuse myself more than anything. I can usually get the       Log On


   

Question 601702: Can someone help me solve these and show all work. I am trying to learn algebra but not doing very good I don't think. I confuse myself more than anything. I can usually get the answers but showing how I got it is another story all together,
1. Solve x^2 = 3x + 5
2. V=3.5√h,for h
(Distance to horizon from a height)
Thank you all for your help.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1. Solve x^2 = 3x + 5
x%5E2+-+3x+-+5+=+0
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%2B-5+=+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%2A-5=29.

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

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+29+%29%29%2F2%5C1+=+4.19258240356725
x%5B2%5D+=+%28-%28-3%29-sqrt%28+29+%29%29%2F2%5C1+=+-1.19258240356725

Quadratic expression 1x%5E2%2B-3x%2B-5 can be factored:
1x%5E2%2B-3x%2B-5+=+%28x-4.19258240356725%29%2A%28x--1.19258240356725%29
Again, the answer is: 4.19258240356725, -1.19258240356725. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-5+%29

-------------
2. V=3.5√h,for h
V^2 = 12.25h
h = V^2/12.25 or
h = 4V^2/49
----------
(Distance to horizon from a height)