SOLUTION: solve by quadratic formula: 4x^2 + 4x + 17 = 0 A=4 B=4 C=17 I solved it and got -4 + or - i SQRT 16 over 8 My question is can this be reduced because there is a -4? So

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: solve by quadratic formula: 4x^2 + 4x + 17 = 0 A=4 B=4 C=17 I solved it and got -4 + or - i SQRT 16 over 8 My question is can this be reduced because there is a -4? So      Log On


   

Question 292979: solve by quadratic formula: 4x^2 + 4x + 17 = 0
A=4
B=4
C=17
I solved it and got -4 + or - i SQRT 16 over 8
My question is can this be reduced because there is a -4? So, I am wondering if this would be -2 + or - i SQRT 16 over 4.
Thank you for your assistance.
Found 2 solutions by jim_thompson5910, edjones:
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%2B4%2Ax%2B17=0 ( notice a=4, b=4, and c=17)





x+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A4%2A17+%29%29%2F%282%2A4%29 Plug in a=4, b=4, and c=17




x+=+%28-4+%2B-+sqrt%28+16-4%2A4%2A17+%29%29%2F%282%2A4%29 Square 4 to get 16




x+=+%28-4+%2B-+sqrt%28+16%2B-272+%29%29%2F%282%2A4%29 Multiply -4%2A17%2A4 to get -272




x+=+%28-4+%2B-+sqrt%28+-256+%29%29%2F%282%2A4%29 Combine like terms in the radicand (everything under the square root)




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




x+=+%28-4+%2B-+16%2Ai%29%2F%288%29 Multiply 2 and 4 to get 8




After simplifying, the quadratic has roots of


x=-1%2F2%2B2%2Ai or x=-1%2F2-2%2Ai

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
4x^2 + 4x + 17 = 0
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B4x%2B17+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A4%2A17=-256.

The discriminant -256 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -256 is + or - sqrt%28+256%29+=+16.

The solution is x%5B12%5D+=+%28-4%2B-+i%2Asqrt%28+-256+%29%29%2F2%5C4+=++%28-4%2B-+i%2A16%29%2F2%5C4+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B4%2Ax%2B17+%29

.
x=-1/2+2i, x=-1/2-2i
.
Ed