Question

square root of 14s+49 =s-7

Answer 1

14s + 49 = s^2 - 14s + 49
28s = s^2
s = 28

Answer 2

square root of t-8 =2t+1

Answer 3

sqrt(t-8)=2t+1
t-8 = (2t + 1)^2
t-8 = (4t^2 + 4t + 1)
4t^2 + 3t + 9 = 0
4[(t^2 + 3t/4) + 9/4] = 0
4[(t + 3/8)^2 - 9/64 + 9/4] = 0
4[(t + 3/8)^2 + (- 9 + 9*16)/64] = 0
4[(t + 3/8)^2 + 135/64] = 0
(t + 3/8)^2 = - 135/64
t+3/8 = +/- sqrt(-135/64)
t = sqrt(-134)/8 - 3/8 and t = -sqrt(-135)/8 - 3/8

Ans. t = sqrt(-134)/8 - 3/8 and t = -sqrt(-135)/8 - 3/8

Answer 4

Note that solutions are not real (i.e. they are complex).