Solve for x.
2 times ( sqrt. of 21-x ) - ( the sqrt of 3x-6) =5
I read that as:
2√(21-x) - √(3x-6) = 5
2√(21-x) = √(3x-6) + 5
square both sides:
4(21-x) = 3x-6 + 10√(3x-6) + 25
84 - 4x = 3x-6 + 10√(3x-6) + 25
65 -7x = 10√(3x-6)
square again
4225 - 910x + 49x^2 = 100(3x-6)
49x^2 - 1210x + 4825 = 0
x = (1210 ±√518400)/98
= 1210 ± 720)/98
= 965/49 or x = 5
I guess we could have factored that to
(x-5)(49x - 965) = 0
since we squared, we MUST verify all answers
if x = 5
LS = 2√16 - √9
= 8 - 3 = 5 = RS... so x = 5 is valid
if x = 965/49 (I used my calculator)
LS = 2.28.. - 7.68.. ≠ 5
so x = 5