SOLUTION: 4x^2+16x+15=0 Solve for x

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 4x^2+16x+15=0 Solve for x      Log On


   

Question 296744: 4x^2+16x+15=0
Solve for x
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%2B16%2Ax%2B15=0 ( notice a=4, b=16, and c=15)





x+=+%28-16+%2B-+sqrt%28+%2816%29%5E2-4%2A4%2A15+%29%29%2F%282%2A4%29 Plug in a=4, b=16, and c=15




x+=+%28-16+%2B-+sqrt%28+256-4%2A4%2A15+%29%29%2F%282%2A4%29 Square 16 to get 256




x+=+%28-16+%2B-+sqrt%28+256%2B-240+%29%29%2F%282%2A4%29 Multiply -4%2A15%2A4 to get -240




x+=+%28-16+%2B-+sqrt%28+16+%29%29%2F%282%2A4%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-16+%2B-+4%29%2F%282%2A4%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-16+%2B-+4%29%2F8 Multiply 2 and 4 to get 8


So now the expression breaks down into two parts


x+=+%28-16+%2B+4%29%2F8 or x+=+%28-16+-+4%29%2F8


Lets look at the first part:


x=%28-16+%2B+4%29%2F8


x=-12%2F8 Add the terms in the numerator

x=-3%2F2 Divide


So one answer is

x=-3%2F2




Now lets look at the second part:


x=%28-16+-+4%29%2F8


x=-20%2F8 Subtract the terms in the numerator

x=-5%2F2 Divide


So another answer is

x=-5%2F2


So our solutions are:

x=-3%2F2 or x=-5%2F2