Question

What is the solution of StartRoot x squared + 49 EndRoot = x + 5?
x = twelve-fifths
x = negative twelve-fifths
x = –6 or x = –3
no solution

Answer 1

Solve sqrt(x^2 + 49) = x + 5. Square both sides (noting x+5 must be ≥ 0):
x^2 + 49 = (x + 5)^2 = x^2 + 10x + 25
Cancel x^2: 49 = 10x + 25 → 10x = 24 → x = 24/10 = 12/5.

Check: x + 5 = 12/5 + 5 = 37/5 > 0, and sqrt((12/5)^2 + 49) = 37/5, so it works.

Answer: x = twelve-fifths.