y^2+2y=11

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Solution for y^2+2y=11 equation:


Simplifying
y2 + 2y = 11

Reorder the terms:
2y + y2 = 11

Solving
2y + y2 = 11

Solving for variable 'y'.

Reorder the terms:
-11 + 2y + y2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 2y + 11 + y2 = 0 + 11

Reorder the terms:
-11 + 11 + 2y + y2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 2y + y2 = 0 + 11
2y + y2 = 0 + 11

Combine like terms: 0 + 11 = 11
2y + y2 = 11

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = 11 + 1

Reorder the terms:
1 + 2y + y2 = 11 + 1

Combine like terms: 11 + 1 = 12
1 + 2y + y2 = 12

Factor a perfect square on the left side:
(y + 1)(y + 1) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(y + 1) equal to 3.464101615 and -3.464101615.

Subproblem 1

y + 1 = 3.464101615 Simplifying y + 1 = 3.464101615 Reorder the terms: 1 + y = 3.464101615 Solving 1 + y = 3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 3.464101615 + -1 Combine like terms: 1 + -1 = 0 0 + y = 3.464101615 + -1 y = 3.464101615 + -1 Combine like terms: 3.464101615 + -1 = 2.464101615 y = 2.464101615 Simplifying y = 2.464101615

Subproblem 2

y + 1 = -3.464101615 Simplifying y + 1 = -3.464101615 Reorder the terms: 1 + y = -3.464101615 Solving 1 + y = -3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -3.464101615 + -1 Combine like terms: 1 + -1 = 0 0 + y = -3.464101615 + -1 y = -3.464101615 + -1 Combine like terms: -3.464101615 + -1 = -4.464101615 y = -4.464101615 Simplifying y = -4.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.464101615, -4.464101615}

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