SOLUTION: 5x^2-32x-21=0

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Question 273827: 5x^2-32x-21=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 5%2Ax%5E2-32%2Ax-21=0 ( notice a=5, b=-32, and c=-21)





x+=+%28--32+%2B-+sqrt%28+%28-32%29%5E2-4%2A5%2A-21+%29%29%2F%282%2A5%29 Plug in a=5, b=-32, and c=-21




x+=+%2832+%2B-+sqrt%28+%28-32%29%5E2-4%2A5%2A-21+%29%29%2F%282%2A5%29 Negate -32 to get 32




x+=+%2832+%2B-+sqrt%28+1024-4%2A5%2A-21+%29%29%2F%282%2A5%29 Square -32 to get 1024 (note: remember when you square -32, you must square the negative as well. This is because %28-32%29%5E2=-32%2A-32=1024.)




x+=+%2832+%2B-+sqrt%28+1024%2B420+%29%29%2F%282%2A5%29 Multiply -4%2A-21%2A5 to get 420




x+=+%2832+%2B-+sqrt%28+1444+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)




x+=+%2832+%2B-+38%29%2F%282%2A5%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2832+%2B-+38%29%2F10 Multiply 2 and 5 to get 10


So now the expression breaks down into two parts


x+=+%2832+%2B+38%29%2F10 or x+=+%2832+-+38%29%2F10


Lets look at the first part:


x=%2832+%2B+38%29%2F10


x=70%2F10 Add the terms in the numerator

x=7 Divide


So one answer is

x=7




Now lets look at the second part:


x=%2832+-+38%29%2F10


x=-6%2F10 Subtract the terms in the numerator

x=-3%2F5 Divide


So another answer is

x=-3%2F5


So our solutions are:

x=7 or x=-3%2F5