15y^2+62y-290=0

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Solution for 15y^2+62y-290=0 equation: 


Simplifying
15y2 + 62y + -290 = 0

Reorder the terms:
-290 + 62y + 15y2 = 0

Solving
-290 + 62y + 15y2 = 0

Solving for variable 'y'.

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

Divide each side by '15'.
-19.33333333 + 4.133333333y + y2 = 0

Move the constant term to the right:

Add '19.33333333' to each side of the equation.
-19.33333333 + 4.133333333y + 19.33333333 + y2 = 0 + 19.33333333

Reorder the terms:
-19.33333333 + 19.33333333 + 4.133333333y + y2 = 0 + 19.33333333

Combine like terms: -19.33333333 + 19.33333333 = 0.00000000
0.00000000 + 4.133333333y + y2 = 0 + 19.33333333
4.133333333y + y2 = 0 + 19.33333333

Combine like terms: 0 + 19.33333333 = 19.33333333
4.133333333y + y2 = 19.33333333

The y term is 4.133333333y.  Take half its coefficient (2.066666667).
Square it (4.271111112) and add it to both sides.

Add '4.271111112' to each side of the equation.
4.133333333y + 4.271111112 + y2 = 19.33333333 + 4.271111112

Reorder the terms:
4.271111112 + 4.133333333y + y2 = 19.33333333 + 4.271111112

Combine like terms: 19.33333333 + 4.271111112 = 23.604444442
4.271111112 + 4.133333333y + y2 = 23.604444442

Factor a perfect square on the left side:
(y + 2.066666667)(y + 2.066666667) = 23.604444442

Calculate the square root of the right side: 4.858440536

Break this problem into two subproblems by setting 
(y + 2.066666667) equal to 4.858440536 and -4.858440536.


Subproblem 1
y + 2.066666667 = 4.858440536

Simplifying
y + 2.066666667 = 4.858440536

Reorder the terms:
2.066666667 + y = 4.858440536

Solving
2.066666667 + y = 4.858440536

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2.066666667' to each side of the equation.
2.066666667 + -2.066666667 + y = 4.858440536 + -2.066666667

Combine like terms: 2.066666667 + -2.066666667 = 0.000000000
0.000000000 + y = 4.858440536 + -2.066666667
y = 4.858440536 + -2.066666667

Combine like terms: 4.858440536 + -2.066666667 = 2.791773869
y = 2.791773869

Simplifying
y = 2.791773869


Subproblem 2
y + 2.066666667 = -4.858440536

Simplifying
y + 2.066666667 = -4.858440536

Reorder the terms:
2.066666667 + y = -4.858440536

Solving
2.066666667 + y = -4.858440536

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2.066666667' to each side of the equation.
2.066666667 + -2.066666667 + y = -4.858440536 + -2.066666667

Combine like terms: 2.066666667 + -2.066666667 = 0.000000000
0.000000000 + y = -4.858440536 + -2.066666667
y = -4.858440536 + -2.066666667

Combine like terms: -4.858440536 + -2.066666667 = -6.925107203
y = -6.925107203

Simplifying
y = -6.925107203


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.791773869, -6.925107203}

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