Question

Determine the solution set of (2x - 5)2 = 11.

Answer 1

Taking square root on both sides, that becomes 2x - 5 = (+/-) √11

Then:

2x = (+/-)√11 + 5

x = [5 +/- √11 ] / 2

x = 5/2 +/- (√11)/2

That is, x = 5/2 +(√11)/2 and x = 5/2 - (√11)/2

Answer 2

I think what you meant was

(2x - 5)² = 11 -- (1)

Square root both sides of (1), i.e.

√(2x - 5)² = ± √11 -- (2)

From (2), we have

2x - 5 = ± √11 -- (3)

By adding 5 to both sides in (3), we have

2x = 5 ± √11 -- (4)

Divide both sides of (4) by 2, and we obtain

x = (5 ± √11)/2 -- (5)

From (5), the solution set of (1) is

x = (5 + √11)/2, (5 - √11)/2 ...Ans.