Question

Solve x-sqrt(1-x)=-5 algebraically.

Answer 1

First up, move the square root over.\[x-\sqrt{1-x}=-5\]\[x+5=\sqrt{1-x}\]Now square both sides. Can you tell me what \((x+5)^2\) is?

Answer 2

x^2+25? or is it x^2+10x+25?

Answer 3

It's the second one.

That means you have that \[x^2+10x+25=1-x\]Now you have the quadratic equation \[x^2+11x+24=0\]This factors easily. Can you factor this yourself as well?

Answer 4

You are amazing!! Yes, I can factor that. It ends up being x+8 and x+3 yes? so x= -8, -3?
but -8 will be extraneous, yes so the answer is -3?

Answer 5

That looks perfect. Good job.