SOLUTION: How do I find the value of y in the equation y^2+4y+4=7?

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Question 174873: How do I find the value of y in the equation y^2+4y+4=7?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

y%5E2%2B4y%2B4=7 Start with the given equation.


y%5E2%2B4y%2B4-7=0 Subtract 7 from both sides.


y%5E2%2B4y-3=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=-3


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-%284%29+%2B-+sqrt%28+%284%29%5E2-4%281%29%28-3%29+%29%29%2F%282%281%29%29 Plug in a=1, b=4, and c=-3


y+=+%28-4+%2B-+sqrt%28+16-4%281%29%28-3%29+%29%29%2F%282%281%29%29 Square 4 to get 16.


y+=+%28-4+%2B-+sqrt%28+16--12+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-3%29 to get -12


y+=+%28-4+%2B-+sqrt%28+16%2B12+%29%29%2F%282%281%29%29 Rewrite sqrt%2816--12%29 as sqrt%2816%2B12%29


y+=+%28-4+%2B-+sqrt%28+28+%29%29%2F%282%281%29%29 Add 16 to 12 to get 28


y+=+%28-4+%2B-+sqrt%28+28+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


y+=+%28-4+%2B-+2%2Asqrt%287%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


y+=+%28-4%29%2F%282%29+%2B-+%282%2Asqrt%287%29%29%2F%282%29 Break up the fraction.


y+=+-2+%2B-+sqrt%287%29 Reduce.


y+=+-2%2Bsqrt%287%29 or y+=+-2-sqrt%287%29 Break up the expression.


So the answers are y+=+-2%2Bsqrt%287%29 or y+=+-2-sqrt%287%29


which approximate to y=0.646 or y=-4.646