Find the the sulotion set/roots of the following equation 1. x(x + 3) = 28
2.3s(s-2) = 12s
3.( t + 1)²+(t - 8) ² = 45

4.(x + 2)² (x - 2)² 16
+ __ = _
5 3 3
5. 4 r
+ = -2
t - 3 2

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