13y^2+2y-35=0

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Solution for 13y^2+2y-35=0 equation:


Simplifying
13y2 + 2y + -35 = 0

Reorder the terms:
-35 + 2y + 13y2 = 0

Solving
-35 + 2y + 13y2 = 0

Solving for variable 'y'.

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

Divide each side by '13'.
-2.692307692 + 0.1538461538y + y2 = 0

Move the constant term to the right:

Add '2.692307692' to each side of the equation.
-2.692307692 + 0.1538461538y + 2.692307692 + y2 = 0 + 2.692307692

Reorder the terms:
-2.692307692 + 2.692307692 + 0.1538461538y + y2 = 0 + 2.692307692

Combine like terms: -2.692307692 + 2.692307692 = 0.000000000
0.000000000 + 0.1538461538y + y2 = 0 + 2.692307692
0.1538461538y + y2 = 0 + 2.692307692

Combine like terms: 0 + 2.692307692 = 2.692307692
0.1538461538y + y2 = 2.692307692

The y term is 0.1538461538y.  Take half its coefficient (0.0769230769).
Square it (0.005917159760) and add it to both sides.

Add '0.005917159760' to each side of the equation.
0.1538461538y + 0.005917159760 + y2 = 2.692307692 + 0.005917159760

Reorder the terms:
0.005917159760 + 0.1538461538y + y2 = 2.692307692 + 0.005917159760

Combine like terms: 2.692307692 + 0.005917159760 = 2.69822485176
0.005917159760 + 0.1538461538y + y2 = 2.69822485176

Factor a perfect square on the left side:
(y + 0.0769230769)(y + 0.0769230769) = 2.69822485176

Calculate the square root of the right side: 1.642627423

Break this problem into two subproblems by setting 
(y + 0.0769230769) equal to 1.642627423 and -1.642627423.

Subproblem 1

y + 0.0769230769 = 1.642627423 Simplifying y + 0.0769230769 = 1.642627423 Reorder the terms: 0.0769230769 + y = 1.642627423 Solving 0.0769230769 + y = 1.642627423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + y = 1.642627423 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + y = 1.642627423 + -0.0769230769 y = 1.642627423 + -0.0769230769 Combine like terms: 1.642627423 + -0.0769230769 = 1.5657043461 y = 1.5657043461 Simplifying y = 1.5657043461

Subproblem 2

y + 0.0769230769 = -1.642627423 Simplifying y + 0.0769230769 = -1.642627423 Reorder the terms: 0.0769230769 + y = -1.642627423 Solving 0.0769230769 + y = -1.642627423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + y = -1.642627423 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + y = -1.642627423 + -0.0769230769 y = -1.642627423 + -0.0769230769 Combine like terms: -1.642627423 + -0.0769230769 = -1.7195504999 y = -1.7195504999 Simplifying y = -1.7195504999

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.5657043461, -1.7195504999}

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