Answer:
To solve for m in the equation:
√(m-1) + 5 = m-2
First, isolate the square root term by subtracting 5 from both sides:
√(m-1) = m-7
Now, square both sides to get rid of the square root:
(m-1) = (m-7)^2
Expand the right side of the equation:
(m-1) = m^2 - 14m + 49
Now, set the equation equal to zero by moving all terms to one side:
m^2 - 15m + 50 = 0
Now, factor the quadratic equation:
(m-10)(m-5) = 0
Therefore, m = 10 or m = 5.
You should always check your solution in the original equation in case of extraneous solutions.
