(7y^2+2y-3)+(2-4y+5y^2)=

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Solution for (7y^2+2y-3)+(2-4y+5y^2)= equation:


Simplifying
(7y2 + 2y + -3) + (2 + -4y + 5y2) = 0

Reorder the terms:
(-3 + 2y + 7y2) + (2 + -4y + 5y2) = 0

Remove parenthesis around (-3 + 2y + 7y2)
-3 + 2y + 7y2 + (2 + -4y + 5y2) = 0

Remove parenthesis around (2 + -4y + 5y2)
-3 + 2y + 7y2 + 2 + -4y + 5y2 = 0

Reorder the terms:
-3 + 2 + 2y + -4y + 7y2 + 5y2 = 0

Combine like terms: -3 + 2 = -1
-1 + 2y + -4y + 7y2 + 5y2 = 0

Combine like terms: 2y + -4y = -2y
-1 + -2y + 7y2 + 5y2 = 0

Combine like terms: 7y2 + 5y2 = 12y2
-1 + -2y + 12y2 = 0

Solving
-1 + -2y + 12y2 = 0

Solving for variable 'y'.

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

Divide each side by '12'.
-0.08333333333 + -0.1666666667y + y2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + -0.1666666667y + 0.08333333333 + y2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + -0.1666666667y + y2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + -0.1666666667y + y2 = 0 + 0.08333333333
-0.1666666667y + y2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
-0.1666666667y + y2 = 0.08333333333

The y term is -0.1666666667y.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667y + 0.006944444447 + y2 = 0.08333333333 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667y + y2 = 0.08333333333 + 0.006944444447

Combine like terms: 0.08333333333 + 0.006944444447 = 0.090277777777
0.006944444447 + -0.1666666667y + y2 = 0.090277777777

Factor a perfect square on the left side:
(y + -0.08333333335)(y + -0.08333333335) = 0.090277777777

Calculate the square root of the right side: 0.300462606

Break this problem into two subproblems by setting 
(y + -0.08333333335) equal to 0.300462606 and -0.300462606.

Subproblem 1

y + -0.08333333335 = 0.300462606 Simplifying y + -0.08333333335 = 0.300462606 Reorder the terms: -0.08333333335 + y = 0.300462606 Solving -0.08333333335 + y = 0.300462606 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + y = 0.300462606 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + y = 0.300462606 + 0.08333333335 y = 0.300462606 + 0.08333333335 Combine like terms: 0.300462606 + 0.08333333335 = 0.38379593935 y = 0.38379593935 Simplifying y = 0.38379593935

Subproblem 2

y + -0.08333333335 = -0.300462606 Simplifying y + -0.08333333335 = -0.300462606 Reorder the terms: -0.08333333335 + y = -0.300462606 Solving -0.08333333335 + y = -0.300462606 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + y = -0.300462606 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + y = -0.300462606 + 0.08333333335 y = -0.300462606 + 0.08333333335 Combine like terms: -0.300462606 + 0.08333333335 = -0.21712927265 y = -0.21712927265 Simplifying y = -0.21712927265

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.38379593935, -0.21712927265}

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