-9+2.5y-0.7y+1+64y^2=

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Solution for -9+2.5y-0.7y+1+64y^2= equation:


Simplifying
-9 + 2.5y + -0.7y + 1 + 64y2 = 0

Reorder the terms:
-9 + 1 + 2.5y + -0.7y + 64y2 = 0

Combine like terms: -9 + 1 = -8
-8 + 2.5y + -0.7y + 64y2 = 0

Combine like terms: 2.5y + -0.7y = 1.8y
-8 + 1.8y + 64y2 = 0

Solving
-8 + 1.8y + 64y2 = 0

Solving for variable 'y'.

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

Divide each side by '64'.
-0.125 + 0.028125y + y2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 0.028125y + 0.125 + y2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 0.028125y + y2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 0.028125y + y2 = 0 + 0.125
0.028125y + y2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
0.028125y + y2 = 0.125

The y term is 0.028125y.  Take half its coefficient (0.0140625).
Square it (0.0001977539063) and add it to both sides.

Add '0.0001977539063' to each side of the equation.
0.028125y + 0.0001977539063 + y2 = 0.125 + 0.0001977539063

Reorder the terms:
0.0001977539063 + 0.028125y + y2 = 0.125 + 0.0001977539063

Combine like terms: 0.125 + 0.0001977539063 = 0.1251977539063
0.0001977539063 + 0.028125y + y2 = 0.1251977539063

Factor a perfect square on the left side:
(y + 0.0140625)(y + 0.0140625) = 0.1251977539063

Calculate the square root of the right side: 0.353832946

Break this problem into two subproblems by setting 
(y + 0.0140625) equal to 0.353832946 and -0.353832946.

Subproblem 1

y + 0.0140625 = 0.353832946 Simplifying y + 0.0140625 = 0.353832946 Reorder the terms: 0.0140625 + y = 0.353832946 Solving 0.0140625 + y = 0.353832946 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.0140625' to each side of the equation. 0.0140625 + -0.0140625 + y = 0.353832946 + -0.0140625 Combine like terms: 0.0140625 + -0.0140625 = 0.0000000 0.0000000 + y = 0.353832946 + -0.0140625 y = 0.353832946 + -0.0140625 Combine like terms: 0.353832946 + -0.0140625 = 0.339770446 y = 0.339770446 Simplifying y = 0.339770446

Subproblem 2

y + 0.0140625 = -0.353832946 Simplifying y + 0.0140625 = -0.353832946 Reorder the terms: 0.0140625 + y = -0.353832946 Solving 0.0140625 + y = -0.353832946 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.0140625' to each side of the equation. 0.0140625 + -0.0140625 + y = -0.353832946 + -0.0140625 Combine like terms: 0.0140625 + -0.0140625 = 0.0000000 0.0000000 + y = -0.353832946 + -0.0140625 y = -0.353832946 + -0.0140625 Combine like terms: -0.353832946 + -0.0140625 = -0.367895446 y = -0.367895446 Simplifying y = -0.367895446

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.339770446, -0.367895446}

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