SOLUTION: Any help on this problem would be great Solve for the variable 2(y – 1)^2 = 4(y + 1)^2 ERic

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Question 296645: Any help on this problem would be great

Solve for the variable
2(y – 1)^2 = 4(y + 1)^2
ERic
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%28y-1%29%5E2+=+4%28y+%2B+1%29%5E2+ Start with the given equation.


2%28y%5E2-2y+%2B+1%29+=+4%28y%5E2%2B2y+%2B+1%29+ FOIL


2y%5E2-4y+%2B+2+=+4y%5E2%2B8y+%2B+4+ Distribute.


0+=+4y%5E2%2B8y+%2B+4-2y%5E2%2B4y-2+ Get everything to one side.


0+=+2y%5E2%2B12y+%2B+2+ Combine like terms.


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for y:


Starting with the general quadratic


ay%5E2%2Bby%2Bc=0


the general solution using the quadratic equation is:


y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 2%2Ay%5E2%2B12%2Ay%2B2=0 ( notice a=2, b=12, and c=2)





y+=+%28-12+%2B-+sqrt%28+%2812%29%5E2-4%2A2%2A2+%29%29%2F%282%2A2%29 Plug in a=2, b=12, and c=2




y+=+%28-12+%2B-+sqrt%28+144-4%2A2%2A2+%29%29%2F%282%2A2%29 Square 12 to get 144




y+=+%28-12+%2B-+sqrt%28+144%2B-16+%29%29%2F%282%2A2%29 Multiply -4%2A2%2A2 to get -16




y+=+%28-12+%2B-+sqrt%28+128+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




y+=+%28-12+%2B-+8%2Asqrt%282%29%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




y+=+%28-12+%2B-+8%2Asqrt%282%29%29%2F4 Multiply 2 and 2 to get 4


So now the expression breaks down into two parts


y+=+%28-12+%2B+8%2Asqrt%282%29%29%2F4 or y+=+%28-12+-+8%2Asqrt%282%29%29%2F4



Now break up the fraction



y=-12%2F4%2B8%2Asqrt%282%29%2F4 or y=-12%2F4-8%2Asqrt%282%29%2F4



Simplify



y=-3%2B2%2Asqrt%282%29 or y=-3-2%2Asqrt%282%29



So the solutions are:

y=-3%2B2%2Asqrt%282%29 or y=-3-2%2Asqrt%282%29