Question

Solve the equation:
\(\sqrt{x - 1} = x - 7\)
@johnyy

Answer 1

First, square both sides:
\((\sqrt{x - 1})^2 = (x - 7)^2\)
\(x - 1 = x^2 - 14x + 49\)
\(0= x^2 - 15x + 50\)
\(0 = (x - 10)(x - 5)\)

Answer 2

x - 10 = 0 or x - 5 = 0
x = 10 or x = 5

Answer 3

Since the equation had to be squared, we must check all solutions in the original equation.
Check x = 10:
\(\sqrt{10 - 1} = 10 - 7\)
\(\sqrt{9} = 3\)
\(3 = 3\) A true statement, so x = 10 is a true solution.