|
Question 700786: (x+5)^2 = -81. What is the final simplified problem? I came up with x=-14, x=-4 but i also got x=-5+9i. I am confused which answer i should have. Thank you for your help
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! I would choose the complex answer seeing you are more into the complex number system now. In fact, I might even advise you include another answer besides this one. In earlier courses of algebra, it was customary to just write "no solution" when we came cross square roots of negative number because we did not know how to use complex numbers. Further support that I have for telling you to write the answer in complex form is by what I found when I tried using the answers you've gotten:
1. x = -4
(-4+5)^2 = -81
(1)^2 = -81
1 does not equal -81.
2. x = -14
(-14+5)^2 = -81
(-9)^2 = -81
81 does not equal -81.
3. x = -5 + 9i
[(-5+9i)+5]^2 = -81
(9i)^2 = -81
(9)^2[(sqrt)(-1]^2 = -81
81(-1) = -81
-81 does equal -81.
Here's my work for rewriting the given function backwards:
(x+5)^2 = -81
(x+5)^2 = (-1)81
(x+5)^2 = (i^2)81
(x+5)^2 = (i^2)(9^2) ***
x+5 = 9i
x = 9i-5
x = -5+9i.
OR
(x+5)^2 = (i^2)(-9)^2 ***
x+5 = -9i
x = -9i-5
x = -5-9i.
(x+5)^2 = -81
(-9i)^2 = -81
(-9)^2(-1) = -81
81(-1) = -81
-81 does equal -81.
As you can see, theoretically -5-9i makes the function true like -5+9i. However, it is dependent on what your teacher expects and what your course teaches. Notwithstanding, the complex answer you have is correct. -5+9i works, but I don't see where -4 and -14 work.
|
|
|
| |
