Solve \sqrt{10-x} + x=8. Enter your solutions in a comma-separated list.

Question

I used the quadratic formula and ended up with-127+-(-215)/2

Answer 1

Did you actually try using your values to see whether they satisfied the equation?

√(10-x) + x = 8
√(10-x) = 8-x
10-x = x^2-16x+64
x^2-15x+54 = 0
(x-9)(x-6) = 0
x = 6 or 9

should have showed your work, so we could see what went wrong.

Answer 2

However, since both sides were squared, all answers must be checked in the original equation
√(10-x) + x = 8

if x = 6
LS = √4 + 6 = 8 = RS

if x = 9
LS = √1 + 9 = 10 ≠ RS

so the only solution is x = 6

Answer 3

I did check the other answer.
Sure enough, √1 + 9 = 10
and I thought, "That's ok."

Good catch. I had expected an extraneous root, and was surprised that there "wasn't" one.