solve the equation: √(x-15) - √(x)= -3

Question

I'm having trouble solving this equation in my College Algebra class because my professor is originally a chemistry professor he likes to solve everything the hard way and I'm really bad at math.

Answer 1

√(x-15)-√x=-3.

Square both sides:

x-15+x-2√(x(x-15))=9,

2x-2√(x(x-15))=24,

x-12=√(x(x-15)),

Square again:

x²-24x+144=x²-15x,

144=9x, x=16.

Now check this result:

√(16-15)-√16=1-4=-3.