5y^2-16y+8=0

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Solution for 5y^2-16y+8=0 equation:


Simplifying
5y2 + -16y + 8 = 0

Reorder the terms:
8 + -16y + 5y2 = 0

Solving
8 + -16y + 5y2 = 0

Solving for variable 'y'.

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

Divide each side by '5'.
1.6 + -3.2y + y2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + -3.2y + -1.6 + y2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + -3.2y + y2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + -3.2y + y2 = 0 + -1.6
-3.2y + y2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
-3.2y + y2 = -1.6

The y term is -3.2y.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2y + 2.56 + y2 = -1.6 + 2.56

Reorder the terms:
2.56 + -3.2y + y2 = -1.6 + 2.56

Combine like terms: -1.6 + 2.56 = 0.96
2.56 + -3.2y + y2 = 0.96

Factor a perfect square on the left side:
(y + -1.6)(y + -1.6) = 0.96

Calculate the square root of the right side: 0.979795897

Break this problem into two subproblems by setting 
(y + -1.6) equal to 0.979795897 and -0.979795897.

Subproblem 1

y + -1.6 = 0.979795897 Simplifying y + -1.6 = 0.979795897 Reorder the terms: -1.6 + y = 0.979795897 Solving -1.6 + y = 0.979795897 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + y = 0.979795897 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + y = 0.979795897 + 1.6 y = 0.979795897 + 1.6 Combine like terms: 0.979795897 + 1.6 = 2.579795897 y = 2.579795897 Simplifying y = 2.579795897

Subproblem 2

y + -1.6 = -0.979795897 Simplifying y + -1.6 = -0.979795897 Reorder the terms: -1.6 + y = -0.979795897 Solving -1.6 + y = -0.979795897 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + y = -0.979795897 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + y = -0.979795897 + 1.6 y = -0.979795897 + 1.6 Combine like terms: -0.979795897 + 1.6 = 0.620204103 y = 0.620204103 Simplifying y = 0.620204103

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.579795897, 0.620204103}

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