SOLUTION: Happy Wednesday all, I would like to request some help with the problem I have listed below. If you could show me all the steps, so that I know how you found the final answer,

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Happy Wednesday all, I would like to request some help with the problem I have listed below. If you could show me all the steps, so that I know how you found the final answer,       Log On


   

Question 362560: Happy Wednesday all,
I would like to request some help with the problem I have listed below. If you could show me all the steps, so that I know how you found the final answer, that would be great! I am at a loss, and confused too.
Section 11.4, #3
Directions: Solve the equation by making an appropriate substitution.

x-512-16√(x ) =0
answer in the book is= 1024 could you help me work it out? thanks!
Answer by HasanSahin(52) About Me  (Show Source):
You can put this solution on YOUR website!
Leave the sqrt part alone firstly;
+16%2Asqrt%28x%29+=+x-512+ Take square of both sides so you'll get;
+256x+=+x%5E2+-1024x+%2B+262144+
+0+=+x%5E2+-1280x+%2B+262144+
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1280x%2B262144+=+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=%28-1280%29%5E2-4%2A1%2A262144=589824.

Discriminant d=589824 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1280%2B-sqrt%28+589824+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1280%29%2Bsqrt%28+589824+%29%29%2F2%5C1+=+1024
x%5B2%5D+=+%28-%28-1280%29-sqrt%28+589824+%29%29%2F2%5C1+=+256

Quadratic expression 1x%5E2%2B-1280x%2B262144 can be factored:
1x%5E2%2B-1280x%2B262144+=+1%28x-1024%29%2A%28x-256%29
Again, the answer is: 1024, 256. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1280%2Ax%2B262144+%29