SOLUTION: I need to solve 4xsqared+3x=0 using the quadratic formula but i dont quite understand the formula can someone help?

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Question 610887: I need to solve 4xsqared+3x=0 using the quadratic formula but i dont quite understand the formula can someone help?
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 4%2Ax%5E2%2B3%2Ax%2B0=0 (note: since the polynomial does not have a constant term, the 3rd coefficient is zero. In other words, c=0. So that means the polynomial really looks like 4%2Ax%5E2%2B3%2Ax%2B0=0 notice a=4, b=3, and c=0)





x+=+%28-3+%2B-+sqrt%28+%283%29%5E2-4%2A4%2A0+%29%29%2F%282%2A4%29 Plug in a=4, b=3, and c=0




x+=+%28-3+%2B-+sqrt%28+9-4%2A4%2A0+%29%29%2F%282%2A4%29 Square 3 to get 9




x+=+%28-3+%2B-+sqrt%28+9%2B0+%29%29%2F%282%2A4%29 Multiply -4%2A0%2A4 to get 0




x+=+%28-3+%2B-+sqrt%28+9+%29%29%2F%282%2A4%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-3+%2B-+3%29%2F%282%2A4%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-3+%2B-+3%29%2F8 Multiply 2 and 4 to get 8


So now the expression breaks down into two parts


x+=+%28-3+%2B+3%29%2F8 or x+=+%28-3+-+3%29%2F8


Lets look at the first part:


x=%28-3+%2B+3%29%2F8


x=0%2F8 Add the terms in the numerator

x=0 Divide


So one answer is

x=0




Now lets look at the second part:


x=%28-3+-+3%29%2F8


x=-6%2F8 Subtract the terms in the numerator

x=-3%2F4 Divide


So another answer is

x=-3%2F4


So our solutions are:

x=0 or x=-3%2F4