8y^2-10y+1=0

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Solution for 8y^2-10y+1=0 equation:


Simplifying
8y2 + -10y + 1 = 0

Reorder the terms:
1 + -10y + 8y2 = 0

Solving
1 + -10y + 8y2 = 0

Solving for variable 'y'.

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

Divide each side by '8'.
0.125 + -1.25y + y2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -1.25y + -0.125 + y2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -1.25y + y2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -1.25y + y2 = 0 + -0.125
-1.25y + y2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-1.25y + y2 = -0.125

The y term is -1.25y.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25y + 0.390625 + y2 = -0.125 + 0.390625

Reorder the terms:
0.390625 + -1.25y + y2 = -0.125 + 0.390625

Combine like terms: -0.125 + 0.390625 = 0.265625
0.390625 + -1.25y + y2 = 0.265625

Factor a perfect square on the left side:
(y + -0.625)(y + -0.625) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(y + -0.625) equal to 0.515388203 and -0.515388203.

Subproblem 1

y + -0.625 = 0.515388203 Simplifying y + -0.625 = 0.515388203 Reorder the terms: -0.625 + y = 0.515388203 Solving -0.625 + y = 0.515388203 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + y = 0.515388203 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + y = 0.515388203 + 0.625 y = 0.515388203 + 0.625 Combine like terms: 0.515388203 + 0.625 = 1.140388203 y = 1.140388203 Simplifying y = 1.140388203

Subproblem 2

y + -0.625 = -0.515388203 Simplifying y + -0.625 = -0.515388203 Reorder the terms: -0.625 + y = -0.515388203 Solving -0.625 + y = -0.515388203 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + y = -0.515388203 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + y = -0.515388203 + 0.625 y = -0.515388203 + 0.625 Combine like terms: -0.515388203 + 0.625 = 0.109611797 y = 0.109611797 Simplifying y = 0.109611797

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.140388203, 0.109611797}

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