2y^2+5y=20.50

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Solution for 2y^2+5y=20.50 equation:


Simplifying
2y2 + 5y = 20.50

Reorder the terms:
5y + 2y2 = 20.50

Solving
5y + 2y2 = 20.50

Solving for variable 'y'.

Reorder the terms:
-20.50 + 5y + 2y2 = 20.50 + -20.50

Combine like terms: 20.50 + -20.50 = 0.00
-20.50 + 5y + 2y2 = 0.00

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

Divide each side by '2'.
-10.25 + 2.5y + y2 = 0.00

Move the constant term to the right:

Add '10.25' to each side of the equation.
-10.25 + 2.5y + 10.25 + y2 = 0.00 + 10.25

Reorder the terms:
-10.25 + 10.25 + 2.5y + y2 = 0.00 + 10.25

Combine like terms: -10.25 + 10.25 = 0.00
0.00 + 2.5y + y2 = 0.00 + 10.25
2.5y + y2 = 0.00 + 10.25

Combine like terms: 0.00 + 10.25 = 10.25
2.5y + y2 = 10.25

The y term is 2.5y.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5y + 1.5625 + y2 = 10.25 + 1.5625

Reorder the terms:
1.5625 + 2.5y + y2 = 10.25 + 1.5625

Combine like terms: 10.25 + 1.5625 = 11.8125
1.5625 + 2.5y + y2 = 11.8125

Factor a perfect square on the left side:
(y + 1.25)(y + 1.25) = 11.8125

Calculate the square root of the right side: 3.436931771

Break this problem into two subproblems by setting 
(y + 1.25) equal to 3.436931771 and -3.436931771.

Subproblem 1

y + 1.25 = 3.436931771 Simplifying y + 1.25 = 3.436931771 Reorder the terms: 1.25 + y = 3.436931771 Solving 1.25 + y = 3.436931771 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + y = 3.436931771 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + y = 3.436931771 + -1.25 y = 3.436931771 + -1.25 Combine like terms: 3.436931771 + -1.25 = 2.186931771 y = 2.186931771 Simplifying y = 2.186931771

Subproblem 2

y + 1.25 = -3.436931771 Simplifying y + 1.25 = -3.436931771 Reorder the terms: 1.25 + y = -3.436931771 Solving 1.25 + y = -3.436931771 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + y = -3.436931771 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + y = -3.436931771 + -1.25 y = -3.436931771 + -1.25 Combine like terms: -3.436931771 + -1.25 = -4.686931771 y = -4.686931771 Simplifying y = -4.686931771

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.186931771, -4.686931771}

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