SOLUTION: √(x-1) = x-7 I need to know the steps to solve this problem and similar ones

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Question 635755: √(x-1) = x-7
I need to know the steps to solve this problem and similar ones
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Ingeneral: 1) isolate radical, 2) square both sides of EQ, 3)solve

Radical already isolate in this ex.

sqrt%28x-1%29+=+%28x-7%29

      x - 1 = x^2 - 14x + 49

     x^2 - 15x + 50 = 0

   (x - 10)(x - 5) = 0

    x = 10  0r  x = 5  (x = 5 being an extraneous solution) as 4  ≠  -2 )

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x-1%29+=+x-7+
%28sqrt%28x-1%29%29%5E2+=+%28x-7%29%5E2+
x-1+=+x%5E2-14x%2B49+
0+=+x%5E2-14x-x%2B1%2B49+...or.......x%5E2-14x-x%2B1%2B49=0+
x%5E2-15x%2B50=0+.....use quadratic formula to solve for x
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-15%29+%2B-+sqrt%28+%28-15%29%5E2-4%2A1%2A50+%29%29%2F%282%2A1%29+
x+=+%2815+%2B-+sqrt%28225-200+%29%29%2F2+
x+=+%2815+%2B-+sqrt%2825+%29%29%2F2+
x+=+%2815+%2B-5%29%2F2+
solutions:
x+=+%2815+%2B5%29%2F2+
x+=+20%2F2+
x+=+10+

or
x+=+%2815+-5%29%2F2+
x+=+10%2F2+
x+=+5+

in your case the only solution that works is x+=+10+