SOLUTION: Please help me solve. Thank you (1-x)^2=9 I think that I am supposed to set it to zero but it somehow isn't working for me.

Algebra ->  Inequalities -> SOLUTION: Please help me solve. Thank you (1-x)^2=9 I think that I am supposed to set it to zero but it somehow isn't working for me.       Log On


   

Question 223590: Please help me solve. Thank you
(1-x)^2=9
I think that I am supposed to set it to zero but it somehow isn't working for me.
Found 2 solutions by checkley77, jsmallt9:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(1-x)^2=9
(1-x)=sqrt9
1-x=3
-x=3-1
-x=2
x=-2 ans.
Proof:
(1-(-2))^2=9
(1+2)^2=9
3^2=9
9=9

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
(Someone else's solution is only "half" of the answer. The error is that
sqrt%28%281-x%29%5E2%29+=+abs%281-x%29 not 1-x.)
%281-x%29%5E2+=+9
Here's a few of ways to solve this:
  • Simple logic:
    1. The equation says that something squared equals nine.
    2. What numbers can be squared and result in a 9? Answer: 3 and -3.
    3. So (1-x) = 3 or (1-x) = -3. Now we just solve each equation:
      1-x = 3 or 1-x = -3
      -x = 2 or -x = -4
      x = 2 or x = 4
  • Clever use of the fact that %281-x%29%5E2+ and 9 are both perfect squares:
    1. Subtract 9 from each side:
      %281-x%29%5E2+-+9+=+0
    2. Factor as a difference of squares:
      %281-x%29%5E2+-+9+=+0
      %281-x%29%5E2+-+3%5E2+=+0
      %28%281-x%29+%2B+3%29%28%281-x%29+-+3%29+=+0
    3. Figure out what x values make the factors 0:
      %281-x%29%2B3+=+0 or %281-x%29-3+=+0
      4-x+=+0 or -2-x+=+0
      -x+=+-4 or -x+=+2
      x+=+4 or x+=+-2
  • Simplify and solve:
    1. Simplify the left side:
      %281-x%29%5E2+=+9
      %281%29%5E2+-2%281%29%28x%29+%2B+%28x%29%5E2+=+9
      x%5E2+-2x+%2B+1+=+9
    2. Solve the equation. Since it is a quadratic equation we'll get one side equal to zero and then factor:
      x%5E2+-2x+-8+=+0
      %28x+-+4%29%28x%2B2%29+=+0
      Now we'll figure out what x values make the factors zero:
      x-4+=+0 or x%2B2+=+0
      x+=+4 or x+=+2

Either way there are two solutions:
x = 4 or x = -2