x^2+11*x+27=0

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Solution for x^2+11*x+27=0 equation:


Simplifying
x2 + 11x + 27 = 0

Reorder the terms:
27 + 11x + x2 = 0

Solving
27 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + 11x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + 11x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 11x + x2 = 0 + -27
11x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
11x + x2 = -27

The x term is 11x.  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.
11x + 30.25 + x2 = -27 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -27 + 30.25

Combine like terms: -27 + 30.25 = 3.25
30.25 + 11x + x2 = 3.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 5.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

x + 5.5 = 1.802775638 Simplifying x + 5.5 = 1.802775638 Reorder the terms: 5.5 + x = 1.802775638 Solving 5.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 1.802775638 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 1.802775638 + -5.5 x = 1.802775638 + -5.5 Combine like terms: 1.802775638 + -5.5 = -3.697224362 x = -3.697224362 Simplifying x = -3.697224362

Subproblem 2

x + 5.5 = -1.802775638 Simplifying x + 5.5 = -1.802775638 Reorder the terms: 5.5 + x = -1.802775638 Solving 5.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -1.802775638 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -1.802775638 + -5.5 x = -1.802775638 + -5.5 Combine like terms: -1.802775638 + -5.5 = -7.302775638 x = -7.302775638 Simplifying x = -7.302775638

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.697224362, -7.302775638}

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