SOLUTION: Please help with this problem 3x^2 + x -4 = 0 What is the solution set ? Thank you

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Question 118752: Please help with this problem 3x^2 + x -4 = 0 What is the solution set ?
Thank you
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 3%2Ax%5E2%2Bx-4=0 ( notice a=3, b=1, and c=-4)




x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A3%2A-4+%29%29%2F%282%2A3%29 Plug in a=3, b=1, and c=-4



x+=+%28-1+%2B-+sqrt%28+1-4%2A3%2A-4+%29%29%2F%282%2A3%29 Square 1 to get 1



x+=+%28-1+%2B-+sqrt%28+1%2B48+%29%29%2F%282%2A3%29 Multiply -4%2A-4%2A3 to get 48



x+=+%28-1+%2B-+sqrt%28+49+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-1+%2B-+7%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-1+%2B-+7%29%2F6 Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

x+=+%28-1+%2B+7%29%2F6 or x+=+%28-1+-+7%29%2F6

Lets look at the first part:

x=%28-1+%2B+7%29%2F6

x=6%2F6 Add the terms in the numerator
x=1 Divide

So one answer is
x=1



Now lets look at the second part:

x=%28-1+-+7%29%2F6

x=-8%2F6 Subtract the terms in the numerator
x=-4%2F3 Divide

So another answer is
x=-4%2F3

So our solutions are:
x=1 or x=-4%2F3

Notice when we graph 3%2Ax%5E2%2Bx-4, we get:

+graph%28+500%2C+500%2C+-14%2C+11%2C+-14%2C+11%2C3%2Ax%5E2%2B1%2Ax%2B-4%29+

and we can see that the roots are x=1 and x=-4%2F3. This verifies our answer