SOLUTION: 96.) Find all real or imaginary solutions. use the method of your choice. sqrt(7x+29=x+3)

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Question 165061This question is from textbook Elementary and Intermediate
: 96.) Find all real or imaginary solutions. use the method of your choice.
sqrt(7x+29=x+3)
This question is from textbook Elementary and Intermediate

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%287x%2B29%29=x%2B3 Start with the given equation


7x%2B29=%28x%2B3%29%5E2 Square both sides to eliminate the square root.


7x%2B29=x%5E2%2B6x%2B9 FOIL the right side.


0=x%5E2%2B6x%2B9-7x-29 Get everything to the right side.


0=x%5E2-x-20 Combine like terms


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-1, and c=-20


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-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-20%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-1, and c=-20


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-20%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%28-20%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--80+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-20%29 to get -80


x+=+%281+%2B-+sqrt%28+1%2B80+%29%29%2F%282%281%29%29 Rewrite sqrt%281--80%29 as sqrt%281%2B80%29


x+=+%281+%2B-+sqrt%28+81+%29%29%2F%282%281%29%29 Add 1 to 80 to get 81


x+=+%281+%2B-+sqrt%28+81+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+9%29%2F%282%29 Take the square root of 81 to get 9.


x+=+%281+%2B+9%29%2F%282%29 or x+=+%281+-+9%29%2F%282%29 Break up the expression.


x+=+%2810%29%2F%282%29 or x+=++%28-8%29%2F%282%29 Combine like terms.


x+=+5 or x+=+-4 Simplify.


So the possible answers are x+=+5 or x+=+-4


However, if you plug in x+=+-4 back into the original equation, you'll find that the solution does not work. So this means that x+=+-4 is NOT a solution.


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Answer:


So the solution is x+=+5