1. explain why the equation (x-4)^2 -28=8 has two solutions. then solve the equation to find the solutions. show your work.

The equation is a second degree equation so it will have 2 solutions.
theeasiest way to solve this equation is the 'square root method'.
first i'll get the 'square on the left and everything else on the right.
(x - 4)^2 -28 = 8
add 28 to both sides.
(x - 4)^2 = 36
take the square root of both sides
x - 4 = + - 6
add 4 to both sides.
x = 4 + - 6
x = 4 + 6 = 10
x = 4 - 6 = -2

(x-4)^2 extended is x^2 - 8x + 16. then you substitute that in and you get x^2 - 8x + 16 - 28 = 8. 16-28= -12. then you subtract 8 on both sides. you get   x^2 - 8x - 12 - 8 = 0. -12-8=-20.   x^2 - 8x - 20 = 0. then you use the quadratic formula and you get the 2 answers.