Question

Solve the equation x2 + 8x – 2 = 0 using both
a. The quadratic formula
b. Completing the square
Write a paragraph or two comparing and contrasting the two methods. Explain which method you prefer and why.
c) Use the accompanying graph to estimate the time at
which the workers are most efficient.
d) Use the accompanying graph to estimate the
maximum number of components assembled per
hour during an 8-hour shift.

Answer 1

formula:
x = (-8 ± √72)/2
= (-8 ± 6√2)/2 = -4 ± 3√2

completing the square

x^2 + 8x = 2
x^2 + 8x + <b>16</b> = 2 + <b>16</b>
(x+4)^2 = 18
x+4 = ± √18 = ±3√2
x = -4 ± 3√2

notice that completing the square gives you the reduced answer.
(If the equation starts with 1x^2 and the x term is even, I always use completing the square instead of the formula)