SOLUTION: Please help solve this problem for me I am having a hard time my instructor is not making it easy. Thank you Solve 2x^-3x-2=0 using quadratic formula. show detail work. Thank y

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Question 112883: Please help solve this problem for me I am having a hard time my instructor is not making it easy. Thank you
Solve 2x^-3x-2=0 using quadratic formula. show detail work. Thank you again
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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

Notice when we graph 2%2Ax%5E2-3%2Ax-2, we get:

+graph%28+500%2C+500%2C+-11%2C+12%2C+-11%2C+12%2C2%2Ax%5E2%2B-3%2Ax%2B-2%29+

and we can see that the roots are x=2 and x=-1%2F2. This verifies our answer