9y^2+24y-64=0

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Solution for 9y^2+24y-64=0 equation: 


Simplifying
9y2 + 24y + -64 = 0

Reorder the terms:
-64 + 24y + 9y2 = 0

Solving
-64 + 24y + 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'.
-7.111111111 + 2.666666667y + y2 = 0

Move the constant term to the right:

Add '7.111111111' to each side of the equation.
-7.111111111 + 2.666666667y + 7.111111111 + y2 = 0 + 7.111111111

Reorder the terms:
-7.111111111 + 7.111111111 + 2.666666667y + y2 = 0 + 7.111111111

Combine like terms: -7.111111111 + 7.111111111 = 0.000000000
0.000000000 + 2.666666667y + y2 = 0 + 7.111111111
2.666666667y + y2 = 0 + 7.111111111

Combine like terms: 0 + 7.111111111 = 7.111111111
2.666666667y + y2 = 7.111111111

The y term is 2.666666667y.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667y + 1.777777780 + y2 = 7.111111111 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667y + y2 = 7.111111111 + 1.777777780

Combine like terms: 7.111111111 + 1.777777780 = 8.888888891
1.777777780 + 2.666666667y + y2 = 8.888888891

Factor a perfect square on the left side:
(y + 1.333333334)(y + 1.333333334) = 8.888888891

Calculate the square root of the right side: 2.98142397

Break this problem into two subproblems by setting 
(y + 1.333333334) equal to 2.98142397 and -2.98142397.


Subproblem 1
y + 1.333333334 = 2.98142397

Simplifying
y + 1.333333334 = 2.98142397

Reorder the terms:
1.333333334 + y = 2.98142397

Solving
1.333333334 + y = 2.98142397

Solving for variable 'y'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + y = 2.98142397 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + y = 2.98142397 + -1.333333334
y = 2.98142397 + -1.333333334

Combine like terms: 2.98142397 + -1.333333334 = 1.648090636
y = 1.648090636

Simplifying
y = 1.648090636


Subproblem 2
y + 1.333333334 = -2.98142397

Simplifying
y + 1.333333334 = -2.98142397

Reorder the terms:
1.333333334 + y = -2.98142397

Solving
1.333333334 + y = -2.98142397

Solving for variable 'y'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + y = -2.98142397 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + y = -2.98142397 + -1.333333334
y = -2.98142397 + -1.333333334

Combine like terms: -2.98142397 + -1.333333334 = -4.314757304
y = -4.314757304

Simplifying
y = -4.314757304


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.648090636, -4.314757304}

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