SOLUTION: I have no idea how to do this one. Solve for the variable: 4(y-1)squared = 8(y+1)squared

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Question 207875: I have no idea how to do this one.
Solve for the variable:
4(y-1)squared = 8(y+1)squared
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4%28y-1%29%5E2=8%28y%2B1%29 Start with the given equation.


4%28y%5E2-2y%2B1%29=8%28y%2B1%29 FOIL


4y%5E2-8y%2B4=8y%2B8 Distribute


4y%5E2-8y%2B4-8y-8=0 Get every term to the left side.


4y%5E2-16y-4=0 Combine like terms.


Notice that the quadratic 4y%5E2-16y-4 is in the form of Ay%5E2%2BBy%2BC where A=4, B=-16, and C=-4


Let's use the quadratic formula to solve for "y":


y+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


y+=+%28-%28-16%29+%2B-+sqrt%28+%28-16%29%5E2-4%284%29%28-4%29+%29%29%2F%282%284%29%29 Plug in A=4, B=-16, and C=-4


y+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%284%29%28-4%29+%29%29%2F%282%284%29%29 Negate -16 to get 16.


y+=+%2816+%2B-+sqrt%28+256-4%284%29%28-4%29+%29%29%2F%282%284%29%29 Square -16 to get 256.


y+=+%2816+%2B-+sqrt%28+256--64+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-4%29 to get -64


y+=+%2816+%2B-+sqrt%28+256%2B64+%29%29%2F%282%284%29%29 Rewrite sqrt%28256--64%29 as sqrt%28256%2B64%29


y+=+%2816+%2B-+sqrt%28+320+%29%29%2F%282%284%29%29 Add 256 to 64 to get 320


y+=+%2816+%2B-+sqrt%28+320+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


y+=+%2816+%2B-+8%2Asqrt%285%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


y+=+%2816%29%2F%288%29+%2B-+%288%2Asqrt%285%29%29%2F%288%29 Break up the fraction.


y+=+2+%2B-+sqrt%285%29 Reduce.


y+=+2%2Bsqrt%285%29 or y+=+2-sqrt%285%29 Break up the expression.


So the solutions are y+=+2%2Bsqrt%285%29 or y+=+2-sqrt%285%29


which approximate to y=4.236 or y=-0.236