SOLUTION: Solve for X 43. (x - 6)^2 = 2x - 9x + 38

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Question 171818: Solve for X
43. (x - 6)^2 = 2x - 9x + 38
Found 2 solutions by jim_thompson5910, checkley77:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-6%29%5E2+=+2x-9x+%2B+38 Start with the given equation


%28x-6%29%5E2+=+-7x+%2B+38 Combine like terms.


x%5E2-12x%2B36+=+-7x+%2B+38 FOIL


x%5E2-12x%2B36+%2B7x-+38=0 Subtract 7x from both sides. Add 38 to both sides.


x%5E2-5x-2=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-5, and c=-2


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%28-2%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-5, and c=-2


x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%28-2%29+%29%29%2F%282%281%29%29 Negate -5 to get 5.


x+=+%285+%2B-+sqrt%28+25-4%281%29%28-2%29+%29%29%2F%282%281%29%29 Square -5 to get 25.


x+=+%285+%2B-+sqrt%28+25--8+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-2%29 to get -8


x+=+%285+%2B-+sqrt%28+25%2B8+%29%29%2F%282%281%29%29 Rewrite sqrt%2825--8%29 as sqrt%2825%2B8%29


x+=+%285+%2B-+sqrt%28+33+%29%29%2F%282%281%29%29 Add 25 to 8 to get 33


x+=+%285+%2B-+sqrt%28+33+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%285%2Bsqrt%2833%29%29%2F%282%29 or x+=+%285-sqrt%2833%29%29%2F%282%29 Break up the expression.


So the answers are x+=+%285%2Bsqrt%2833%29%29%2F%282%29 or x+=+%285-sqrt%2833%29%29%2F%282%29


which approximate to x=5.372 or x=-0.372

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(x-6)^2=2x-9x+38
x^2-12x+36=-7x+38
x^2-12x+7x+36-38=0
x^2-5x-2=0
Solving this equation we get irrational roots.
IF you meant:
(x-6)^2=2x^2-9x+38 Then:
x^2-12x+36=2x^2-9x+38
x^2-2x^2-12x+9x+36-38=0
-x^2-3x-2=0 multiply by -1:
x^2+3x+2=0
(x+2)(x+1)=0
x+2=0
x=-2 ans
x+1=0
x=-1 ans.
Proofs:
(-2-6)^2=2*-2^2-9*-2+38
-8*2=2*4+18+38
64=8+18=38
64=64
(-1-6)^2=2*-1^2-9*-1+38
-7^2=2*1+9+38
49=2+9+38
49=49