9y^2-66y+97=0

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Solution for 9y^2-66y+97=0 equation: 


Simplifying
9y2 + -66y + 97 = 0

Reorder the terms:
97 + -66y + 9y2 = 0

Solving
97 + -66y + 9y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
10.77777778 + -7.333333333y + y2 = 0

Move the constant term to the right:

Add '-10.77777778' to each side of the equation.
10.77777778 + -7.333333333y + -10.77777778 + y2 = 0 + -10.77777778

Reorder the terms:
10.77777778 + -10.77777778 + -7.333333333y + y2 = 0 + -10.77777778

Combine like terms: 10.77777778 + -10.77777778 = 0.00000000
0.00000000 + -7.333333333y + y2 = 0 + -10.77777778
-7.333333333y + y2 = 0 + -10.77777778

Combine like terms: 0 + -10.77777778 = -10.77777778
-7.333333333y + y2 = -10.77777778

The y term is -7.333333333y.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333y + 13.44444445 + y2 = -10.77777778 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333y + y2 = -10.77777778 + 13.44444445

Combine like terms: -10.77777778 + 13.44444445 = 2.66666667
13.44444445 + -7.333333333y + y2 = 2.66666667

Factor a perfect square on the left side:
(y + -3.666666667)(y + -3.666666667) = 2.66666667

Calculate the square root of the right side: 1.632993163

Break this problem into two subproblems by setting 
(y + -3.666666667) equal to 1.632993163 and -1.632993163.


Subproblem 1
y + -3.666666667 = 1.632993163

Simplifying
y + -3.666666667 = 1.632993163

Reorder the terms:
-3.666666667 + y = 1.632993163

Solving
-3.666666667 + y = 1.632993163

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + y = 1.632993163 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + y = 1.632993163 + 3.666666667
y = 1.632993163 + 3.666666667

Combine like terms: 1.632993163 + 3.666666667 = 5.29965983
y = 5.29965983

Simplifying
y = 5.29965983


Subproblem 2
y + -3.666666667 = -1.632993163

Simplifying
y + -3.666666667 = -1.632993163

Reorder the terms:
-3.666666667 + y = -1.632993163

Solving
-3.666666667 + y = -1.632993163

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + y = -1.632993163 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + y = -1.632993163 + 3.666666667
y = -1.632993163 + 3.666666667

Combine like terms: -1.632993163 + 3.666666667 = 2.033673504
y = 2.033673504

Simplifying
y = 2.033673504


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.29965983, 2.033673504}

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