-8y(y-5)=7y-8

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Solution for -8y(y-5)=7y-8 equation:


Simplifying
-8y(y + -5) = 7y + -8

Reorder the terms:
-8y(-5 + y) = 7y + -8
(-5 * -8y + y * -8y) = 7y + -8
(40y + -8y2) = 7y + -8

Reorder the terms:
40y + -8y2 = -8 + 7y

Solving
40y + -8y2 = -8 + 7y

Solving for variable 'y'.

Reorder the terms:
8 + 40y + -7y + -8y2 = -8 + 7y + 8 + -7y

Combine like terms: 40y + -7y = 33y
8 + 33y + -8y2 = -8 + 7y + 8 + -7y

Reorder the terms:
8 + 33y + -8y2 = -8 + 8 + 7y + -7y

Combine like terms: -8 + 8 = 0
8 + 33y + -8y2 = 0 + 7y + -7y
8 + 33y + -8y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
8 + 33y + -8y2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1 + -4.125y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4.125y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + -4.125y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4.125y + y2 = 0 + 1
-4.125y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4.125y + y2 = 1

The y term is -4.125y.  Take half its coefficient (-2.0625).
Square it (4.25390625) and add it to both sides.

Add '4.25390625' to each side of the equation.
-4.125y + 4.25390625 + y2 = 1 + 4.25390625

Reorder the terms:
4.25390625 + -4.125y + y2 = 1 + 4.25390625

Combine like terms: 1 + 4.25390625 = 5.25390625
4.25390625 + -4.125y + y2 = 5.25390625

Factor a perfect square on the left side:
(y + -2.0625)(y + -2.0625) = 5.25390625

Calculate the square root of the right side: 2.292140103

Break this problem into two subproblems by setting 
(y + -2.0625) equal to 2.292140103 and -2.292140103.

Subproblem 1

y + -2.0625 = 2.292140103 Simplifying y + -2.0625 = 2.292140103 Reorder the terms: -2.0625 + y = 2.292140103 Solving -2.0625 + y = 2.292140103 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + y = 2.292140103 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + y = 2.292140103 + 2.0625 y = 2.292140103 + 2.0625 Combine like terms: 2.292140103 + 2.0625 = 4.354640103 y = 4.354640103 Simplifying y = 4.354640103

Subproblem 2

y + -2.0625 = -2.292140103 Simplifying y + -2.0625 = -2.292140103 Reorder the terms: -2.0625 + y = -2.292140103 Solving -2.0625 + y = -2.292140103 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + y = -2.292140103 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + y = -2.292140103 + 2.0625 y = -2.292140103 + 2.0625 Combine like terms: -2.292140103 + 2.0625 = -0.229640103 y = -0.229640103 Simplifying y = -0.229640103

Solution

The solution to the problem is based on the solutions from the subproblems. y = {4.354640103, -0.229640103}

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