SOLUTION: how do I solve - x2 - 6x + 16 = 0 It says there are no real answers, but that there are complex answers. What does this mean please? Thank you.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: how do I solve - x2 - 6x + 16 = 0 It says there are no real answers, but that there are complex answers. What does this mean please? Thank you.      Log On


   

Question 128762: how do I solve -
x2 - 6x + 16 = 0
It says there are no real answers, but that there are complex answers. What does this mean please?
Thank you.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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 x%5E2-6%2Ax%2B16=0 ( notice a=1, b=-6, and c=16)




x+=+%28--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A16+%29%29%2F%282%2A1%29 Plug in a=1, b=-6, and c=16



x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A16+%29%29%2F%282%2A1%29 Negate -6 to get 6



x+=+%286+%2B-+sqrt%28+36-4%2A1%2A16+%29%29%2F%282%2A1%29 Square -6 to get 36 (note: remember when you square -6, you must square the negative as well. This is because %28-6%29%5E2=-6%2A-6=36.)



x+=+%286+%2B-+sqrt%28+36%2B-64+%29%29%2F%282%2A1%29 Multiply -4%2A16%2A1 to get -64



x+=+%286+%2B-+sqrt%28+-28+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%286+%2B-+2%2Ai%2Asqrt%287%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%286+%2B-+2%2Ai%2Asqrt%287%29%29%2F%282%29 Multiply 2 and 1 to get 2



After simplifying, the quadratic has roots of

x=3+%2B+sqrt%287%29i or x=3+-+sqrt%287%29i

Notice if we graph the quadratic y=x%5E2-6%2Ax%2B16, we get

+graph%28+500%2C+500%2C+-12%2C+18%2C+-8%2C+22%2C+x%5E2-6%2Ax%2B16%29+ graph of y=x%5E2-6%2Ax%2B16

And we can see that there are no real roots


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
how do I solve -
x^2 - 6x + 16 = 0
It says there are no real answers, but that there are complex answers. What does this mean please?
--------------------
The Real Numbers include the Rational Numbers and the Irrational Numbers.
Complex Numbers are a set of numbers that look like a+bi and where the
a and the b are Real numbers and "i" is the square root of negative-one.
-------------------
Your Problem:
x^2 - 6x + 16 = 0
Use the Quadratic formula to get:
x = [6 +- sqrt(36 - 4*16)]/2
x = [6 +- sqrt(-28)]/2
x = [6 +- 2isqrt(7)]/2
x = [3 +- isqrt(7)]
x = 3+isqrt(7) or x = 3-isqrt(7)
=========================
Notice that the "3" is rational, and the sqrt(7) is irrational
and the answers are in the form a+bi
=========================================
Cheers,
Stan H.
Cheers,
Stan H.