SOLUTION: a(a+1)-3(a+1)=a+1

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Question 200869: a(a+1)-3(a+1)=a+1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a%28a%2B1%29-3%28a%2B1%29=a%2B1 Start with the given equation.


a%5E2%2Ba-3a-3=a%2B1 Distribute


a%5E2%2Ba-3a-3-a=1 Subtract "a" from both sides.


a%5E2%2Ba-3a-3-a-1=0 Subtract 1 from both sides.


a%5E2-3a-4=0 Combine like terms.


Notice that the quadratic a%5E2-3a-4 is in the form of Aa%5E2%2BBa%2BC where A=1, B=-3, and C=-4


Let's use the quadratic formula to solve for "a":


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


a+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-4%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-3, and C=-4


a+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-4%29+%29%29%2F%282%281%29%29 Negate -3 to get 3.


a+=+%283+%2B-+sqrt%28+9-4%281%29%28-4%29+%29%29%2F%282%281%29%29 Square -3 to get 9.


a+=+%283+%2B-+sqrt%28+9--16+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-4%29 to get -16


a+=+%283+%2B-+sqrt%28+9%2B16+%29%29%2F%282%281%29%29 Rewrite sqrt%289--16%29 as sqrt%289%2B16%29


a+=+%283+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29 Add 9 to 16 to get 25


a+=+%283+%2B-+sqrt%28+25+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


a+=+%283+%2B-+5%29%2F%282%29 Take the square root of 25 to get 5.


a+=+%283+%2B+5%29%2F%282%29 or a+=+%283+-+5%29%2F%282%29 Break up the expression.


a+=+%288%29%2F%282%29 or a+=++%28-2%29%2F%282%29 Combine like terms.


a+=+4 or a+=+-1 Simplify.


So the solutions are a+=+4 or a+=+-1