9y^2-160y+469=0

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Solution for 9y^2-160y+469=0 equation:


Simplifying
9y2 + -160y + 469 = 0

Reorder the terms:
469 + -160y + 9y2 = 0

Solving
469 + -160y + 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'.
52.11111111 + -17.77777778y + y2 = 0

Move the constant term to the right:

Add '-52.11111111' to each side of the equation.
52.11111111 + -17.77777778y + -52.11111111 + y2 = 0 + -52.11111111

Reorder the terms:
52.11111111 + -52.11111111 + -17.77777778y + y2 = 0 + -52.11111111

Combine like terms: 52.11111111 + -52.11111111 = 0.00000000
0.00000000 + -17.77777778y + y2 = 0 + -52.11111111
-17.77777778y + y2 = 0 + -52.11111111

Combine like terms: 0 + -52.11111111 = -52.11111111
-17.77777778y + y2 = -52.11111111

The y term is -17.77777778y.  Take half its coefficient (-8.88888889).
Square it (79.01234570) and add it to both sides.

Add '79.01234570' to each side of the equation.
-17.77777778y + 79.01234570 + y2 = -52.11111111 + 79.01234570

Reorder the terms:
79.01234570 + -17.77777778y + y2 = -52.11111111 + 79.01234570

Combine like terms: -52.11111111 + 79.01234570 = 26.90123459
79.01234570 + -17.77777778y + y2 = 26.90123459

Factor a perfect square on the left side:
(y + -8.88888889)(y + -8.88888889) = 26.90123459

Calculate the square root of the right side: 5.18664001

Break this problem into two subproblems by setting 
(y + -8.88888889) equal to 5.18664001 and -5.18664001.

Subproblem 1

y + -8.88888889 = 5.18664001 Simplifying y + -8.88888889 = 5.18664001 Reorder the terms: -8.88888889 + y = 5.18664001 Solving -8.88888889 + y = 5.18664001 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.88888889' to each side of the equation. -8.88888889 + 8.88888889 + y = 5.18664001 + 8.88888889 Combine like terms: -8.88888889 + 8.88888889 = 0.00000000 0.00000000 + y = 5.18664001 + 8.88888889 y = 5.18664001 + 8.88888889 Combine like terms: 5.18664001 + 8.88888889 = 14.0755289 y = 14.0755289 Simplifying y = 14.0755289

Subproblem 2

y + -8.88888889 = -5.18664001 Simplifying y + -8.88888889 = -5.18664001 Reorder the terms: -8.88888889 + y = -5.18664001 Solving -8.88888889 + y = -5.18664001 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.88888889' to each side of the equation. -8.88888889 + 8.88888889 + y = -5.18664001 + 8.88888889 Combine like terms: -8.88888889 + 8.88888889 = 0.00000000 0.00000000 + y = -5.18664001 + 8.88888889 y = -5.18664001 + 8.88888889 Combine like terms: -5.18664001 + 8.88888889 = 3.70224888 y = 3.70224888 Simplifying y = 3.70224888

Solution

The solution to the problem is based on the solutions from the subproblems. y = {14.0755289, 3.70224888}

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