-9+2.4y-0.7y+1+6.4y^2=0

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Solution for -9+2.4y-0.7y+1+6.4y^2=0 equation: 


Simplifying
-9 + 2.4y + -0.7y + 1 + 6.4y2 = 0

Reorder the terms:
-9 + 1 + 2.4y + -0.7y + 6.4y2 = 0

Combine like terms: -9 + 1 = -8
-8 + 2.4y + -0.7y + 6.4y2 = 0

Combine like terms: 2.4y + -0.7y = 1.7y
-8 + 1.7y + 6.4y2 = 0

Solving
-8 + 1.7y + 6.4y2 = 0

Solving for variable 'y'.

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

Divide each side by '6.4'.
-1.25 + 0.265625y + y2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 0.265625y + 1.25 + y2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 0.265625y + y2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 0.265625y + y2 = 0 + 1.25
0.265625y + y2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
0.265625y + y2 = 1.25

The y term is 0.265625y.  Take half its coefficient (0.1328125).
Square it (0.01763916016) and add it to both sides.

Add '0.01763916016' to each side of the equation.
0.265625y + 0.01763916016 + y2 = 1.25 + 0.01763916016

Reorder the terms:
0.01763916016 + 0.265625y + y2 = 1.25 + 0.01763916016

Combine like terms: 1.25 + 0.01763916016 = 1.26763916016
0.01763916016 + 0.265625y + y2 = 1.26763916016

Factor a perfect square on the left side:
(y + 0.1328125)(y + 0.1328125) = 1.26763916016

Calculate the square root of the right side: 1.125894826

Break this problem into two subproblems by setting 
(y + 0.1328125) equal to 1.125894826 and -1.125894826.


Subproblem 1
y + 0.1328125 = 1.125894826

Simplifying
y + 0.1328125 = 1.125894826

Reorder the terms:
0.1328125 + y = 1.125894826

Solving
0.1328125 + y = 1.125894826

Solving for variable 'y'.

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

Add '-0.1328125' to each side of the equation.
0.1328125 + -0.1328125 + y = 1.125894826 + -0.1328125

Combine like terms: 0.1328125 + -0.1328125 = 0.0000000
0.0000000 + y = 1.125894826 + -0.1328125
y = 1.125894826 + -0.1328125

Combine like terms: 1.125894826 + -0.1328125 = 0.993082326
y = 0.993082326

Simplifying
y = 0.993082326


Subproblem 2
y + 0.1328125 = -1.125894826

Simplifying
y + 0.1328125 = -1.125894826

Reorder the terms:
0.1328125 + y = -1.125894826

Solving
0.1328125 + y = -1.125894826

Solving for variable 'y'.

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

Add '-0.1328125' to each side of the equation.
0.1328125 + -0.1328125 + y = -1.125894826 + -0.1328125

Combine like terms: 0.1328125 + -0.1328125 = 0.0000000
0.0000000 + y = -1.125894826 + -0.1328125
y = -1.125894826 + -0.1328125

Combine like terms: -1.125894826 + -0.1328125 = -1.258707326
y = -1.258707326

Simplifying
y = -1.258707326


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.993082326, -1.258707326}

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