Question

(a) Complete the square by writing in the form . Note: the numbers and can be positive or negative.

x^2-14x-17=(x-7)^2+

(b) Solve the equation by completing the square or using the quadratic formula. If there is more than one correct answer, enter your answers as a comma separated list. If there are no solutions, enter NONE.

x^2-14x-17=0

I keep getting this wrong but I don't know why.help please

Answer 1

x^2 - 14x + .... = 17 + ....
x^2 - 14x <b>+ 49</b> = 17<b>+ 49</b>
(x-7)^2 = 66
x-7 = ± √66
x = 7 ± √66

by formula:
x = (14 ± √(14^2 - 4(1)(-17))/2
= (14 ± √264)/2
= (14 ± 2√66)/2
= 7 ± √66

When the coefficient of x^2 is 1 and the middle term is even, I always use "completing the square" rather than the formula. Notice you get the answer already in simplified form