SOLUTION: Solve the following equation for A:2/A=8+4A

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Question 202657: Solve the following equation for A:2/A=8+4A
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Fa=8%2B4a Start with the given equation.


2=a%288%2B4a%29 Multiply both sides by "a".


2=8a%2B4a%5E2 Distribute


0=8a%2B4a%5E2-2 Subtract 2 from both sides.


0=4a%5E2%2B8a-2 Rearrange the terms.


Notice that the quadratic 4a%5E2%2B8a-2 is in the form of Aa%5E2%2BBa%2BC where A=4, B=8, and C=-2


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-%288%29+%2B-+sqrt%28+%288%29%5E2-4%284%29%28-2%29+%29%29%2F%282%284%29%29 Plug in A=4, B=8, and C=-2


a+=+%28-8+%2B-+sqrt%28+64-4%284%29%28-2%29+%29%29%2F%282%284%29%29 Square 8 to get 64.


a+=+%28-8+%2B-+sqrt%28+64--32+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-2%29 to get -32


a+=+%28-8+%2B-+sqrt%28+64%2B32+%29%29%2F%282%284%29%29 Rewrite sqrt%2864--32%29 as sqrt%2864%2B32%29


a+=+%28-8+%2B-+sqrt%28+96+%29%29%2F%282%284%29%29 Add 64 to 32 to get 96


a+=+%28-8+%2B-+sqrt%28+96+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


a+=+%28-8+%2B-+4%2Asqrt%286%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


a+=+%28-8%2B4%2Asqrt%286%29%29%2F%288%29 or a+=+%28-8-4%2Asqrt%286%29%29%2F%288%29 Break up the expression.


a+=+%28-2%2Bsqrt%286%29%29%2F%282%29 or a+=+%28-2%2Bsqrt%286%29%29%2F%282%29 Reduce


So the solutions are a+=+%28-2%2Bsqrt%286%29%29%2F%282%29 or a+=+%28-2%2Bsqrt%286%29%29%2F%282%29


which approximate to a=0.225 or a=-2.225