SOLUTION: Solve the equation, x^2+2x=-17 One of the following answers is correct. Which one is it? A) x=2 +or- 8i B) x=-5, x=3 C) x=-1 +or-4i D) x=-1 +or- 3(square root of 2)

Algebra ->  Equations -> SOLUTION: Solve the equation, x^2+2x=-17 One of the following answers is correct. Which one is it? A) x=2 +or- 8i B) x=-5, x=3 C) x=-1 +or-4i D) x=-1 +or- 3(square root of 2)      Log On


   

Question 1198779: Solve the equation, x^2+2x=-17
One of the following answers is correct. Which one is it?
A) x=2 +or- 8i
B) x=-5, x=3
C) x=-1 +or-4i
D) x=-1 +or- 3(square root of 2)
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

Why don't you apply the quadratic formula ?



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation, x^2+2x=-17
----------------
x^2 + 2x + 1 = -16
(x+1)^2 = -16
x+1 = sqrt(-16)
x = -1 + 4i, -1 - 4i
====================================
x^2 + 2x + 17 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%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=%282%29%5E2-4%2A1%2A17=-64.

The discriminant -64 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 -64 is + or - sqrt%28+64%29+=+8.

The solution is x%5B12%5D+=+%28-2%2B-i%2Asqrt%28+-64+%29%29%2F2%5C1+=++%28-2%2B-i%2A8%29%2F2%5C1+, or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B17+%29