SOLUTION: Find all complex-number solutions 2x^2-3x-5=0 I just need to see steps on how to break this down. I know the first part is adding 5 to make C.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find all complex-number solutions 2x^2-3x-5=0 I just need to see steps on how to break this down. I know the first part is adding 5 to make C.       Log On


   

Question 1027646: Find all complex-number solutions
2x^2-3x-5=0
I just need to see steps on how to break this down. I know the first part is adding 5 to make C.

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Not necessarily the first step; some flexibility is possible in the steps.

If you EXPECT complex solutions, then either solve using Completing the Square, or go directly to the general solution of a quadratic formula. You are maybe intent on Completing The Square, since you mention "first part is adding 5...".

2%28x%5E2-3x%2F2-5%2F2%29=0
2%28x%5E2-3x%2F2%2B%283%2F%282%2A2%29%29%5E2-%283%2F%282%2A2%29%29%5E2-5%2F2%29=0
2%28x%5E2-3x%2F2-%283%2F4%29%5E2-9%2F16-5%2F2%29=0
You should recognize what that was....
2%28%28x-3%2F4%29%5E2-9%2F16-5%2F2%29=0
2%28%28x-3%2F4%29%5E2-9%2F16-5%2A8%2F16%29=0
2%28%28x-3%2F4%29%5E2-14%2F16%29=0
2%28x-3%2F4%29%5E2-2%2A14%2F16=0
2%28x-3%2F4%29%5E2-14%2F8=0
2%28x-3%2F4%29%5E2-7%2F4=0
...but, multiply left and right members by 1%2F2...
%28x-3%2F4%29%5E2-7%2F8=0
%28x-3%2F4%29%5E2=7%2F8-------solution will not contain an Imaginary part.
x-3%2F4=0%2B-+sqrt%287%2F8%29
x=-3%2F4%2B-+sqrt%287%2F8%29
x=-3%2F4%2B-+sqrt%287%2A8%29%2F8
x=-3%2F4%2B-+2%2Asqrt%287%2A2%29%2F%282%2A4%29
highlight%28x=-3%2F4%2B-+sqrt%2814%29%2F4%29

As a way of checking quality of the result, find the discriminant on the original equation.
%28-3%29%5E2-4%2A2%2A%28-5%29
9%2B8%2A5
49, A POSITIVE NUMBER, so you expect two REAL solutions for x.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Find all complex-number solutions
2x^2-3x-5=0
I just need to see steps on how to break this down. I know the first part is adding 5 to make C. 
Why would you want to add 5. Are you supposed to solve this by completing the square? If not, the trinomial can be factored as:

(2x - 5)(x + 1) = 0

2x - 5 = 0        OR         x + 1 = 0

highlight_green%28matrix%281%2C7%2C+x%2C+%22=%22%2C+5%2F2%2C+OR%2C+x%2C+%22=%22%2C+-+1%29%29. You are done!!

As seen there are NO COMPLEX-NUMBER solutions.