10y^2+13y-2=

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Solution for 10y^2+13y-2= equation:


Simplifying
10y2 + 13y + -2 = 0

Reorder the terms:
-2 + 13y + 10y2 = 0

Solving
-2 + 13y + 10y2 = 0

Solving for variable 'y'.

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

Divide each side by '10'.
-0.2 + 1.3y + y2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 1.3y + 0.2 + y2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 1.3y + y2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 1.3y + y2 = 0 + 0.2
1.3y + y2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
1.3y + y2 = 0.2

The y term is 1.3y.  Take half its coefficient (0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
1.3y + 0.4225 + y2 = 0.2 + 0.4225

Reorder the terms:
0.4225 + 1.3y + y2 = 0.2 + 0.4225

Combine like terms: 0.2 + 0.4225 = 0.6225
0.4225 + 1.3y + y2 = 0.6225

Factor a perfect square on the left side:
(y + 0.65)(y + 0.65) = 0.6225

Calculate the square root of the right side: 0.788986692

Break this problem into two subproblems by setting 
(y + 0.65) equal to 0.788986692 and -0.788986692.

Subproblem 1

y + 0.65 = 0.788986692 Simplifying y + 0.65 = 0.788986692 Reorder the terms: 0.65 + y = 0.788986692 Solving 0.65 + y = 0.788986692 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + y = 0.788986692 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + y = 0.788986692 + -0.65 y = 0.788986692 + -0.65 Combine like terms: 0.788986692 + -0.65 = 0.138986692 y = 0.138986692 Simplifying y = 0.138986692

Subproblem 2

y + 0.65 = -0.788986692 Simplifying y + 0.65 = -0.788986692 Reorder the terms: 0.65 + y = -0.788986692 Solving 0.65 + y = -0.788986692 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + y = -0.788986692 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + y = -0.788986692 + -0.65 y = -0.788986692 + -0.65 Combine like terms: -0.788986692 + -0.65 = -1.438986692 y = -1.438986692 Simplifying y = -1.438986692

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.138986692, -1.438986692}

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