2y^2-10y+9=0

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Solution for 2y^2-10y+9=0 equation:


Simplifying
2y2 + -10y + 9 = 0

Reorder the terms:
9 + -10y + 2y2 = 0

Solving
9 + -10y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
4.5 + -5y + y2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -5y + -4.5 + y2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -5y + y2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -5y + y2 = 0 + -4.5
-5y + y2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-5y + y2 = -4.5

The y term is -5y.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5y + 6.25 + y2 = -4.5 + 6.25

Reorder the terms:
6.25 + -5y + y2 = -4.5 + 6.25

Combine like terms: -4.5 + 6.25 = 1.75
6.25 + -5y + y2 = 1.75

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(y + -2.5) equal to 1.322875656 and -1.322875656.

Subproblem 1

y + -2.5 = 1.322875656 Simplifying y + -2.5 = 1.322875656 Reorder the terms: -2.5 + y = 1.322875656 Solving -2.5 + y = 1.322875656 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 1.322875656 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 1.322875656 + 2.5 y = 1.322875656 + 2.5 Combine like terms: 1.322875656 + 2.5 = 3.822875656 y = 3.822875656 Simplifying y = 3.822875656

Subproblem 2

y + -2.5 = -1.322875656 Simplifying y + -2.5 = -1.322875656 Reorder the terms: -2.5 + y = -1.322875656 Solving -2.5 + y = -1.322875656 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -1.322875656 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -1.322875656 + 2.5 y = -1.322875656 + 2.5 Combine like terms: -1.322875656 + 2.5 = 1.177124344 y = 1.177124344 Simplifying y = 1.177124344

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.822875656, 1.177124344}

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