25y^2+20y-108=0

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Solution for 25y^2+20y-108=0 equation:


Simplifying
25y2 + 20y + -108 = 0

Reorder the terms:
-108 + 20y + 25y2 = 0

Solving
-108 + 20y + 25y2 = 0

Solving for variable 'y'.

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

Divide each side by '25'.
-4.32 + 0.8y + y2 = 0

Move the constant term to the right:

Add '4.32' to each side of the equation.
-4.32 + 0.8y + 4.32 + y2 = 0 + 4.32

Reorder the terms:
-4.32 + 4.32 + 0.8y + y2 = 0 + 4.32

Combine like terms: -4.32 + 4.32 = 0.00
0.00 + 0.8y + y2 = 0 + 4.32
0.8y + y2 = 0 + 4.32

Combine like terms: 0 + 4.32 = 4.32
0.8y + y2 = 4.32

The y term is 0.8y.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8y + 0.16 + y2 = 4.32 + 0.16

Reorder the terms:
0.16 + 0.8y + y2 = 4.32 + 0.16

Combine like terms: 4.32 + 0.16 = 4.48
0.16 + 0.8y + y2 = 4.48

Factor a perfect square on the left side:
(y + 0.4)(y + 0.4) = 4.48

Calculate the square root of the right side: 2.116601049

Break this problem into two subproblems by setting 
(y + 0.4) equal to 2.116601049 and -2.116601049.

Subproblem 1

y + 0.4 = 2.116601049 Simplifying y + 0.4 = 2.116601049 Reorder the terms: 0.4 + y = 2.116601049 Solving 0.4 + y = 2.116601049 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = 2.116601049 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = 2.116601049 + -0.4 y = 2.116601049 + -0.4 Combine like terms: 2.116601049 + -0.4 = 1.716601049 y = 1.716601049 Simplifying y = 1.716601049

Subproblem 2

y + 0.4 = -2.116601049 Simplifying y + 0.4 = -2.116601049 Reorder the terms: 0.4 + y = -2.116601049 Solving 0.4 + y = -2.116601049 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = -2.116601049 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = -2.116601049 + -0.4 y = -2.116601049 + -0.4 Combine like terms: -2.116601049 + -0.4 = -2.516601049 y = -2.516601049 Simplifying y = -2.516601049

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.716601049, -2.516601049}

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