Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

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Question 151318: y-2-8 sqrt(y-2)+15=0: y-2-8 sqrt(y-2)+15=0
Answer by jim_thompson5910(9166) About Me  (Show Source):
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y-2-8*sqrt(y-2)+15=0 Start with the given equation.


y-8*sqrt(y-2)+13=0 Combine like terms.


y-8*sqrt(y-2)=-13 Subtract 13 from both sides.


-8*sqrt(y-2)=-13-y Subtract y from both sides.


64(y-2)=(-13-y)^2 Square both sides.


64(y-2)=169+26y+y^2 FOIL


64y-128=169+26y+y^2 Distribute


0=169+26y+y^2-64y+128 Subtract 64y from both sides. Add 128 to both sides.


0=y^2-38y+297 Combine like terms


Notice we have a quadratic equation in the form of ay^2+by+c where a=1, b=-38, and c=297


Let's use the quadratic formula to solve for y


y = (-b +- sqrt( b^2-4ac ))/(2a) Start with the quadratic formula


y = (-(-38) +- sqrt( (-38)^2-4(1)(297) ))/(2(1)) Plug in a=1, b=-38, and c=297


y = (38 +- sqrt( (-38)^2-4(1)(297) ))/(2(1)) Negate -38 to get 38.


y = (38 +- sqrt( 1444-4(1)(297) ))/(2(1)) Square -38 to get 1444.


y = (38 +- sqrt( 1444-1188 ))/(2(1)) Multiply 4(1)(297) to get 1188


y = (38 +- sqrt( 256 ))/(2(1)) Subtract 1188 from 1444 to get 256


y = (38 +- sqrt( 256 ))/(2) Multiply 2 and 1 to get 2.


y = (38 +- 16)/(2) Take the square root of 256 to get 16.


y = (38 + 16)/(2) or y = (38 - 16)/(2) Break up the expression.


y = (54)/(2) or y = (22)/(2) Combine like terms.


y = 27 or y = 11 Simplify.


So our answers are y = 27 or y = 11