y^2-3y-11=0

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


Simplifying
y2 + -3y + -11 = 0

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

Solving
-11 + -3y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 11 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 11 + 2.25

Combine like terms: 11 + 2.25 = 13.25
2.25 + -3y + y2 = 13.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(y + -1.5) equal to 3.640054945 and -3.640054945.

Subproblem 1

y + -1.5 = 3.640054945 Simplifying y + -1.5 = 3.640054945 Reorder the terms: -1.5 + y = 3.640054945 Solving -1.5 + y = 3.640054945 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 3.640054945 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 3.640054945 + 1.5 y = 3.640054945 + 1.5 Combine like terms: 3.640054945 + 1.5 = 5.140054945 y = 5.140054945 Simplifying y = 5.140054945

Subproblem 2

y + -1.5 = -3.640054945 Simplifying y + -1.5 = -3.640054945 Reorder the terms: -1.5 + y = -3.640054945 Solving -1.5 + y = -3.640054945 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -3.640054945 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -3.640054945 + 1.5 y = -3.640054945 + 1.5 Combine like terms: -3.640054945 + 1.5 = -2.140054945 y = -2.140054945 Simplifying y = -2.140054945

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.140054945, -2.140054945}

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