Question

Solve by completing the square? Could you please work it out step-by-step?

Answer 1

16 n^2 -10n + 129 = 8n^2 -8

We collect the terms:
8n^2 -10n + 137 = 0

The steps for completing the square:

1) Move the "non X" (or "non N") term to the right:

8n^2 -10n  = -137

2) Divide the equation by the coefficient of N² which in this case is 8
n^2 -1.2n = -17.125

3) Take the coefficient of "N"; divide it by 2; square it; add it to both sides of the equation.
-1.2 / 2 = -.6
-.6^2 = .36


n^2 -1.2n +.36 = -17.125 +.36

Take the square root of both sides:
(n-.6)*(n-.6) = sq root( -16.765 )
That's about as far as I can go.