SOLUTION: I think this is quadratic equation...Please help. Thank you Y^2-4y+4=36 What is the exact solution What is the approximate solution

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Question 176363: I think this is quadratic equation...Please help. Thank you
Y^2-4y+4=36
What is the exact solution
What is the approximate solution
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

y%5E2-4y%2B4=36 Start with the given equation.


y%5E2-4y%2B4-36=0 Subtract 36 from both sides.


y%5E2-4y-32=0 Combine like terms.


Notice we have a quadratic equation in the form of ay%5E2%2Bby%2Bc where a=1, b=-4, and c=-32


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-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%28-32%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-4, and c=-32


y+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%28-32%29+%29%29%2F%282%281%29%29 Negate -4 to get 4.


y+=+%284+%2B-+sqrt%28+16-4%281%29%28-32%29+%29%29%2F%282%281%29%29 Square -4 to get 16.


y+=+%284+%2B-+sqrt%28+16--128+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-32%29 to get -128


y+=+%284+%2B-+sqrt%28+16%2B128+%29%29%2F%282%281%29%29 Rewrite sqrt%2816--128%29 as sqrt%2816%2B128%29


y+=+%284+%2B-+sqrt%28+144+%29%29%2F%282%281%29%29 Add 16 to 128 to get 144


y+=+%284+%2B-+sqrt%28+144+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


y+=+%284+%2B-+12%29%2F%282%29 Take the square root of 144 to get 12.


y+=+%284+%2B+12%29%2F%282%29 or y+=+%284+-+12%29%2F%282%29 Break up the expression.


y+=+%2816%29%2F%282%29 or y+=++%28-8%29%2F%282%29 Combine like terms.


y+=+8 or y+=+-4 Simplify.


So the answers are y+=+8 or y+=+-4

Note: the exact solutions and the approximate solutions are the same (since no approximation is not needed).