SOLUTION: i need help solve 2x^2-3x-2=0 using the quadratic formula

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Question 111570: i need help solve 2x^2-3x-2=0 using the quadratic formula
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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 2%2Ax%5E2-3%2Ax-2=0 ( notice a=2, b=-3, and c=-2)





x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A-2+%29%29%2F%282%2A2%29 Plug in a=2, b=-3, and c=-2




x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A-2+%29%29%2F%282%2A2%29 Negate -3 to get 3




x+=+%283+%2B-+sqrt%28+9-4%2A2%2A-2+%29%29%2F%282%2A2%29 Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because %28-3%29%5E2=-3%2A-3=9.)




x+=+%283+%2B-+sqrt%28+9%2B16+%29%29%2F%282%2A2%29 Multiply -4%2A-2%2A2 to get 16




x+=+%283+%2B-+sqrt%28+25+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%283+%2B-+5%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%283+%2B-+5%29%2F4 Multiply 2 and 2 to get 4


So now the expression breaks down into two parts


x+=+%283+%2B+5%29%2F4 or x+=+%283+-+5%29%2F4


Lets look at the first part:


x=%283+%2B+5%29%2F4


x=8%2F4 Add the terms in the numerator

x=2 Divide


So one answer is

x=2




Now lets look at the second part:


x=%283+-+5%29%2F4


x=-2%2F4 Subtract the terms in the numerator

x=-1%2F2 Divide


So another answer is

x=-1%2F2


So our solutions are:

x=2 or x=-1%2F2