SOLUTION: Solve by completing the square. y^2 - 12y = -11

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Solve by completing the square. y^2 - 12y = -11      Log On


   

Question 189904: Solve by completing the square.

y^2 - 12y = -11
Found 2 solutions by nerdybill, jim_thompson5910:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
y^2 - 12y = -11
(y^2 - 12y + __ ) = -11
where the blank is 1/2 time 'b' squared:
(y^2 - 12y + 36 ) = -11 + 36
(y^2 - 12y + 36 ) = 25
(y^2 - 6)^2 = 25
Take the square root of both sides:
y^2 - 6 = 5
y^2 = 11
y = sqrt(11)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y%5E2+-+12y+=+-11 Start with the given equation.


y%5E2+-+12y+%2B11=0 Add 11 to both sides.


y%5E2-12y%2B11 Start with the left side of the equation.


Take half of the y coefficient -12 to get -6. In other words, %281%2F2%29%28-12%29=-6.


Now square -6 to get 36. In other words, %28-6%29%5E2=%28-6%29%28-6%29=36


y%5E2-12y%2Bhighlight%2836-36%29%2B11 Now add and subtract 36. Make sure to place this after the "y" term. Notice how 36-36=0. So the expression is not changed.


%28y%5E2-12y%2B36%29-36%2B11 Group the first three terms.


%28y-6%29%5E2-36%2B11 Factor y%5E2-12y%2B36 to get %28y-6%29%5E2.


%28y-6%29%5E2-25 Combine like terms.


So after completing the square, y%5E2-12y%2B11 transforms to %28y-6%29%5E2-25. So y%5E2-12y%2B11=%28y-6%29%5E2-25.


So y%5E2-12y%2B11=0 is equivalent to %28y-6%29%5E2-25=0.


-------------------------------------------------------------


%28y-6%29%5E2-25=0 Start with the given equation.


%28y-6%29%5E2=0%2B25Add 25 to both sides.


%28y-6%29%5E2=25 Combine like terms.


x-6=%22%22%2B-sqrt%2825%29 Take the square root of both sides.


y-6=sqrt%2825%29 or y-6=-sqrt%2825%29 Break up the "plus/minus" to form two equations.


y-6=5 or y-6=-5 Take the square root of 25 to get 5.


y=6%2B5 or y=6-5 Add 6 to both sides.


y=11 or y=1 Combine like terms.


--------------------------------------


Answer:


So the solutions are y=11 or y=1.