Question

I would really appreciate if someone were to answer this and show their process! I've already tried 'no solutions', 'all real numbers', and x=0, however, none of them were correct.

Solve the equation. (remember about domain).
sqrt(x^2−10x+25) =x−5

Answer 1

Input:

sqrt(x^2 - 10 x + 25) = x - 5

Plot:

Plot

Alternate forms:

sqrt((x - 5)^2) + 5 = x

sqrt((x - 5)^2) = x - 5

sqrt((x - 5)^2) - x = -5

Alternate form assuming x is positive:

x = abs(x - 5) + 5

Number line:

Number line

Integer solution:

x>=5

Explanation: