1.
x^2 + 3x = 28
x^2 + 3x - 28 = 0
(x + 7)(x - 4) = 0
Therefore,
x = -7 or 4
2.
3s^2 -6s = 12s
3s^2 - 18s = 0
s(s - 6) = 0
Therefore,
s = 0 or 6
3.
t^2 + 2t + 1 + t^2 -16t + 64 = 45
2t^2-14t + 20 = 0
t^2 -7t + 10 = 0
(t - 5)(t - 2) = 0
Therefore, t = 5 or 2
4 .
3(x^2 + 4x + 4) + 5(x^2 - 4x + 4) = 80
8x^2-8x + 32 = 80
x^ 2 - x + 4 = 10
x^2 - x - 6 = 0
(x - 3)(x + 2) = 0
Therefore,
x = 3 or -2
5.
since r and t are close on the keyboard, I can assume one was a typo, but it wouldn’t matter which.
8 + t(t-3) = -4(t-3)
8 + t^2 - 3t + 4t - 12 = 0
t^2 + t - 4 = 0
Using the quadratic formula,
t = (-1+-sqrt(1^2 -4(1)(-4)))/2(1)
t = (-1+-sqrt(17))/2
