SOLUTION: Hi, How would you solve this problem (x-3)^2= 2x^2-7x-21 Thanks.

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Question 177299: Hi, How would you solve this problem
(x-3)^2= 2x^2-7x-21
Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-3%29%5E2=+2x%5E2-7x-21 Start with the given equation.


x%5E2-6x%2B9=+2x%5E2-7x-21 FOIL


x%5E2-6x%2B9-2x%5E2%2B7x%2B21=0 Get all terms to the left side.


-x%5E2%2Bx%2B30=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=-1, b=1, and c=30


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-%281%29+%2B-+sqrt%28+%281%29%5E2-4%28-1%29%2830%29+%29%29%2F%282%28-1%29%29 Plug in a=-1, b=1, and c=30


x+=+%28-1+%2B-+sqrt%28+1-4%28-1%29%2830%29+%29%29%2F%282%28-1%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--120+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%2830%29 to get -120


x+=+%28-1+%2B-+sqrt%28+1%2B120+%29%29%2F%282%28-1%29%29 Rewrite sqrt%281--120%29 as sqrt%281%2B120%29


x+=+%28-1+%2B-+sqrt%28+121+%29%29%2F%282%28-1%29%29 Add 1 to 120 to get 121


x+=+%28-1+%2B-+sqrt%28+121+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


x+=+%28-1+%2B-+11%29%2F%28-2%29 Take the square root of 121 to get 11.


x+=+%28-1+%2B+11%29%2F%28-2%29 or x+=+%28-1+-+11%29%2F%28-2%29 Break up the expression.


x+=+%2810%29%2F%28-2%29 or x+=++%28-12%29%2F%28-2%29 Combine like terms.


x+=+-5 or x+=+6 Simplify.


So the answers are x+=+-5 or x+=+6