SOLUTION: Can you please show me all the steps on how to find all solutions of this equation? {{{ 36t^4 + 29t^2 - 7 = 0 }}} Thank you so much! If you could give me my answer by 10:00

Algebra ->  Equations -> SOLUTION: Can you please show me all the steps on how to find all solutions of this equation? {{{ 36t^4 + 29t^2 - 7 = 0 }}} Thank you so much! If you could give me my answer by 10:00       Log On


   

Question 481490: Can you please show me all the steps on how to find all solutions of this equation?
+36t%5E4+%2B+29t%5E2+-+7+=+0+
Thank you so much!
If you could give me my answer by 10:00 PM tonight that would be great!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
+36t%5E4+%2B+29t%5E2+-+7+=+0+
Sub x for t^2
36x%5E2+%2B+29x+-+7+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 36x%5E2%2B29x%2B-7+=+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=%2829%29%5E2-4%2A36%2A-7=1849.

Discriminant d=1849 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-29%2B-sqrt%28+1849+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2829%29%2Bsqrt%28+1849+%29%29%2F2%5C36+=+0.194444444444444
x%5B2%5D+=+%28-%2829%29-sqrt%28+1849+%29%29%2F2%5C36+=+-1

Quadratic expression 36x%5E2%2B29x%2B-7 can be factored:
36x%5E2%2B29x%2B-7+=+%28x-0.194444444444444%29%2A%28x--1%29
Again, the answer is: 0.194444444444444, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+36%2Ax%5E2%2B29%2Ax%2B-7+%29

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x = t^2 = 7/36
t = +sqrt(7)/6, -sqrt(7)/6
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x = t^2 = -1
t = -i, i