SOLUTION: (b) (3x+2) (9x+3) = 81

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Question 167783: (b) (3x+2) (9x+3) = 81
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%2B2%29+%289x%2B3%29+=+81 Start with the given equation


27x%5E2%2B27x%2B6+=+81 FOIL


27x%5E2%2B27x%2B6-81=0 Subtract 81 from both sides.


27x%5E2%2B27x-75=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=27, b=27, and c=-75


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-%2827%29+%2B-+sqrt%28+%2827%29%5E2-4%2827%29%28-75%29+%29%29%2F%282%2827%29%29 Plug in a=27, b=27, and c=-75


x+=+%28-27+%2B-+sqrt%28+729-4%2827%29%28-75%29+%29%29%2F%282%2827%29%29 Square 27 to get 729.


x+=+%28-27+%2B-+sqrt%28+729--8100+%29%29%2F%282%2827%29%29 Multiply 4%2827%29%28-75%29 to get -8100


x+=+%28-27+%2B-+sqrt%28+729%2B8100+%29%29%2F%282%2827%29%29 Rewrite sqrt%28729--8100%29 as sqrt%28729%2B8100%29


x+=+%28-27+%2B-+sqrt%28+8829+%29%29%2F%282%2827%29%29 Add 729 to 8100 to get 8829


x+=+%28-27+%2B-+sqrt%28+8829+%29%29%2F%2854%29 Multiply 2 and 27 to get 54.


x+=+%28-27+%2B-+9%2Asqrt%28109%29%29%2F%2854%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-27%2B9%2Asqrt%28109%29%29%2F%2854%29 or x+=+%28-27-9%2Asqrt%28109%29%29%2F%2854%29 Break up the expression.


So the answers are x+=+%28-27%2B9%2Asqrt%28109%29%29%2F%2854%29 or x+=+%28-27-9%2Asqrt%28109%29%29%2F%2854%29


which approximate to x=1.24 or x=-2.24