y^2+11y+3=0

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Solution for y^2+11y+3=0 equation:


Simplifying
y2 + 11y + 3 = 0

Reorder the terms:
3 + 11y + y2 = 0

Solving
3 + 11y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 11y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + 11y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 11y + y2 = 0 + -3
11y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
11y + y2 = -3

The y term is 11y.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11y + 30.25 + y2 = -3 + 30.25

Reorder the terms:
30.25 + 11y + y2 = -3 + 30.25

Combine like terms: -3 + 30.25 = 27.25
30.25 + 11y + y2 = 27.25

Factor a perfect square on the left side:
(y + 5.5)(y + 5.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(y + 5.5) equal to 5.220153254 and -5.220153254.

Subproblem 1

y + 5.5 = 5.220153254 Simplifying y + 5.5 = 5.220153254 Reorder the terms: 5.5 + y = 5.220153254 Solving 5.5 + y = 5.220153254 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = 5.220153254 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = 5.220153254 + -5.5 y = 5.220153254 + -5.5 Combine like terms: 5.220153254 + -5.5 = -0.279846746 y = -0.279846746 Simplifying y = -0.279846746

Subproblem 2

y + 5.5 = -5.220153254 Simplifying y + 5.5 = -5.220153254 Reorder the terms: 5.5 + y = -5.220153254 Solving 5.5 + y = -5.220153254 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = -5.220153254 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = -5.220153254 + -5.5 y = -5.220153254 + -5.5 Combine like terms: -5.220153254 + -5.5 = -10.720153254 y = -10.720153254 Simplifying y = -10.720153254

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-0.279846746, -10.720153254}

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