SOLUTION: 6x^2-x-5 solve for x

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Question 165720: 6x^2-x-5 solve for x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I assume that the equation is really 6x%5E2-x-5=0

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 6%2Ax%5E2-x-5=0 ( notice a=6, b=-1, and c=-5)





x+=+%28--1+%2B-+sqrt%28+%28-1%29%5E2-4%2A6%2A-5+%29%29%2F%282%2A6%29 Plug in a=6, b=-1, and c=-5




x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%2A6%2A-5+%29%29%2F%282%2A6%29 Negate -1 to get 1




x+=+%281+%2B-+sqrt%28+1-4%2A6%2A-5+%29%29%2F%282%2A6%29 Square -1 to get 1 (note: remember when you square -1, you must square the negative as well. This is because %28-1%29%5E2=-1%2A-1=1.)




x+=+%281+%2B-+sqrt%28+1%2B120+%29%29%2F%282%2A6%29 Multiply -4%2A-5%2A6 to get 120




x+=+%281+%2B-+sqrt%28+121+%29%29%2F%282%2A6%29 Combine like terms in the radicand (everything under the square root)




x+=+%281+%2B-+11%29%2F%282%2A6%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%281+%2B-+11%29%2F12 Multiply 2 and 6 to get 12


So now the expression breaks down into two parts


x+=+%281+%2B+11%29%2F12 or x+=+%281+-+11%29%2F12


Lets look at the first part:


x=%281+%2B+11%29%2F12


x=12%2F12 Add the terms in the numerator

x=1 Divide


So one answer is

x=1




Now lets look at the second part:


x=%281+-+11%29%2F12


x=-10%2F12 Subtract the terms in the numerator

x=-5%2F6 Divide


So another answer is

x=-5%2F6


So our solutions are:

x=1 or x=-5%2F6