Hello from MrBillDoesMath!
Answer:
_ = (-4) ^2 (Which equals 16)
Discussion:
Generally
(x + a) ^ 2 = x^2 + 2ax + a^2
Note that the constant term in this perfect square equals the square of (1/2) the coefficient of x. Applying the fact to your equation, gives
x^2 - 8x + _ = -1 + _ => -8/2 = -4
x^2 - 8x + (-4)^2 = -1 + (-4)^2 =>
(x -4)^2 = - 1 + 16 = 15 =>
(x-4)^2 = 15 =>
x-4 = +\- sqrt(15) =>
x = 4 +\- sqrt(15)
Thank you,
MrB
