SOLUTION: Solve by completing the square. y^2

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

Question 189904: Solve by completing the square.

y^2 - 12y = -11
Found 2 solutions by nerdybill, jim_thompson5910:
Answer by nerdybill(7384) (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) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Add 11 to both sides.

Start with the left side of the equation.

Take half of the coefficient to get . In other words, .

Now square to get . In other words,

Now add and subtract . Make sure to place this after the "y" term. Notice how . So the expression is not changed.

Group the first three terms.

Factor to get .

Combine like terms.

So after completing the square, transforms to . So .

So is equivalent to .

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Start with the given equation.

Add to both sides.

Combine like terms.

Take the square root of both sides.

or Break up the "plus/minus" to form two equations.

or Take the square root of to get .

or Add to both sides.

or Combine like terms.

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Answer:

So the solutions are or .

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