x^2-11x-27=0

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Solution for x^2-11x-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 = 57.25
30.25 + -11x + x2 = 57.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 57.25

Calculate the square root of the right side: 7.566372975

Break this problem into two subproblems by setting 
(x + -5.5) equal to 7.566372975 and -7.566372975.

Subproblem 1

x + -5.5 = 7.566372975 Simplifying x + -5.5 = 7.566372975 Reorder the terms: -5.5 + x = 7.566372975 Solving -5.5 + x = 7.566372975 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 = 7.566372975 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 7.566372975 + 5.5 x = 7.566372975 + 5.5 Combine like terms: 7.566372975 + 5.5 = 13.066372975 x = 13.066372975 Simplifying x = 13.066372975

Subproblem 2

x + -5.5 = -7.566372975 Simplifying x + -5.5 = -7.566372975 Reorder the terms: -5.5 + x = -7.566372975 Solving -5.5 + x = -7.566372975 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 = -7.566372975 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -7.566372975 + 5.5 x = -7.566372975 + 5.5 Combine like terms: -7.566372975 + 5.5 = -2.066372975 x = -2.066372975 Simplifying x = -2.066372975

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.066372975, -2.066372975}

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