x(x)+11x-1=0

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Solution for x(x)+11x-1=0 equation:


Simplifying
x(x) + 11x + -1 = 0

Multiply x * x
x2 + 11x + -1 = 0

Reorder the terms:
-1 + 11x + x2 = 0

Solving
-1 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 11x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 11x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 11x + x2 = 0 + 1
11x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
11x + x2 = 1

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 = 1 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 1 + 30.25

Combine like terms: 1 + 30.25 = 31.25
30.25 + 11x + x2 = 31.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(x + 5.5) equal to 5.590169944 and -5.590169944.

Subproblem 1

x + 5.5 = 5.590169944 Simplifying x + 5.5 = 5.590169944 Reorder the terms: 5.5 + x = 5.590169944 Solving 5.5 + x = 5.590169944 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 = 5.590169944 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 5.590169944 + -5.5 x = 5.590169944 + -5.5 Combine like terms: 5.590169944 + -5.5 = 0.090169944 x = 0.090169944 Simplifying x = 0.090169944

Subproblem 2

x + 5.5 = -5.590169944 Simplifying x + 5.5 = -5.590169944 Reorder the terms: 5.5 + x = -5.590169944 Solving 5.5 + x = -5.590169944 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 = -5.590169944 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -5.590169944 + -5.5 x = -5.590169944 + -5.5 Combine like terms: -5.590169944 + -5.5 = -11.090169944 x = -11.090169944 Simplifying x = -11.090169944

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.090169944, -11.090169944}

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