SOLUTION: (b) (l + 2) (l – 4) = 20 cm2, find l

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Question 167792: (b) (l + 2) (l – 4) = 20 cm2, find l
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm replacing "l" with "x" (since "l" is often confused with 1)


%28x+%2B+2%29+%28x-4%29+=+20 Start with the given equation


x%5E2-2x-8+=+20 FOIL


x%5E2-2x-8+-+20=0 Subtract 20 from both sides.


x%5E2-2x-28=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-2, and c=-28


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


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


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


x+=+%282+%2B-+sqrt%28+4--112+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-28%29 to get -112


x+=+%282+%2B-+sqrt%28+4%2B112+%29%29%2F%282%281%29%29 Rewrite sqrt%284--112%29 as sqrt%284%2B112%29


x+=+%282+%2B-+sqrt%28+116+%29%29%2F%282%281%29%29 Add 4 to 112 to get 116


x+=+%282+%2B-+sqrt%28+116+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%282+%2B-+2%2Asqrt%2829%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%29%2F%282%29+%2B-+%282%2Asqrt%2829%29%29%2F%282%29 Break up the fraction.


x+=+1+%2B-+1%2Asqrt%2829%29 Reduce.


x+=+1%2Bsqrt%2829%29 or x+=+1-sqrt%2829%29 Break up the expression.


So the possible answers are x+=+1%2Bsqrt%2829%29 or x+=+1-sqrt%2829%29


which approximate to x=6.385 or x=-4.385


Since we're looking for a measurement, and a negative measurement doesn't make much sense, this means that the only answer is x+=+1%2Bsqrt%2829%29 which approximates to x=6.385


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(L + 2) (L – 4) = 20 cm2, find L
------------
L^2-2L-8 = 20
L^2-2L-28 = 0
L = [2 +- sqrt(4-4*1*-28)]/2
L = [2 +- sqrt(116)]/2
L = [2 +- 2sqrt(29)]/2
L = 1+sqrt(29) or x = 1-sqrt(29)
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Cheers,
Stan H.