SOLUTION: Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION x^3 − 7x^2 + 6x − 47 = x^2

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION x^3 − 7x^2 + 6x − 47 = x^2      Log On


   

Question 756600: Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION
x^3 − 7x^2 + 6x − 47 = x^2 + 1
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
x^3 − 7x^2 + 6x − 47 = x^2 + 1
:
x^3 - 7x^2 - x^2 + 6x - 47 - 1 = 0
:
x^3 - 8x^2 + 6x - 48 = 0
Group factor
x^2(x - 8) + 6(x - 8) = 0
Factor out (x-8)
(x - 8)(x^2 + 6) = 0
Solutions
x = 8, the only real solution
and
x^2 = -6; non-real solutions
x = +/-sqrt%28-6%29
x = + i%2Asqrt%286%29
x = - i%2Asqrt%286%29
:
:
Check in original problem with x=8
x^3 - 7x^2 + 6x - 47 = x^2 + 1
8^3 - 7(8^2) + 6(8) - 47 = 8^2 + 1
512 - 448 + 48 - 47 = 64 + 1
65 = 65; confirms our solution