(5y^2-3y+2)+(-6y^2+7y+1)=

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Solution for (5y^2-3y+2)+(-6y^2+7y+1)= equation:


Simplifying
(5y2 + -3y + 2) + (-6y2 + 7y + 1) = 0

Reorder the terms:
(2 + -3y + 5y2) + (-6y2 + 7y + 1) = 0

Remove parenthesis around (2 + -3y + 5y2)
2 + -3y + 5y2 + (-6y2 + 7y + 1) = 0

Reorder the terms:
2 + -3y + 5y2 + (1 + 7y + -6y2) = 0

Remove parenthesis around (1 + 7y + -6y2)
2 + -3y + 5y2 + 1 + 7y + -6y2 = 0

Reorder the terms:
2 + 1 + -3y + 7y + 5y2 + -6y2 = 0

Combine like terms: 2 + 1 = 3
3 + -3y + 7y + 5y2 + -6y2 = 0

Combine like terms: -3y + 7y = 4y
3 + 4y + 5y2 + -6y2 = 0

Combine like terms: 5y2 + -6y2 = -1y2
3 + 4y + -1y2 = 0

Solving
3 + 4y + -1y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3 + -4y + y2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -4y + 3 + y2 = 0 + 3

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

Combine like terms: -3 + 3 = 0
0 + -4y + y2 = 0 + 3
-4y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
-4y + y2 = 3

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 3 + 4

Reorder the terms:
4 + -4y + y2 = 3 + 4

Combine like terms: 3 + 4 = 7
4 + -4y + y2 = 7

Factor a perfect square on the left side:
(y + -2)(y + -2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(y + -2) equal to 2.645751311 and -2.645751311.

Subproblem 1

y + -2 = 2.645751311 Simplifying y + -2 = 2.645751311 Reorder the terms: -2 + y = 2.645751311 Solving -2 + y = 2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + y = 2.645751311 + 2 y = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 y = 4.645751311 Simplifying y = 4.645751311

Subproblem 2

y + -2 = -2.645751311 Simplifying y + -2 = -2.645751311 Reorder the terms: -2 + y = -2.645751311 Solving -2 + y = -2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + y = -2.645751311 + 2 y = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 y = -0.645751311 Simplifying y = -0.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. y = {4.645751311, -0.645751311}

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