John L. answered • 02/19/21
Tutor
New to Wyzant
Naval Academy graduate with more than 10 years experience in teaching
If the problem were this, it would be relatively straight forward to solve, no?
u^2 – 2u -35 = 0. By factoring the polynomial, you would arrive at (u-7)(u+5) = 0. Then by the zero product rule, either (u-7) = 0 or (u+5) = 0. This means that u = 7 or u = -5.
Now..what if u = x^2-6x. for the above to be true, either x^2 -6x = 7 or x^2 -6x = -5. Solve each one by themselves:
x^2 -6x = 7
x^2 -6x – 7 = 0
(x-7)(x+1) = 0
X = 7 or x = -1
Similarly,
x^2 -6x = -5
x^2 -6x + 5 = 0
(x-3)(x-2) = 0
So x = 3, or x = 2. You have four solutions.
Tae M.
-3 and -2 don't add up to -6, so the correct answer would be 7, -1, 5,1... Since -5 times -1 equals the positive five then set both of them equal to zero and you get the 5 and 1.02/19/21