(x)(x)+11x-104=0

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Solution for (x)(x)+11x-104=0 equation:


Simplifying
(x)(x) + 11x + -104 = 0

Multiply x * x
x2 + 11x + -104 = 0

Reorder the terms:
-104 + 11x + x2 = 0

Solving
-104 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '104' to each side of the equation.
-104 + 11x + 104 + x2 = 0 + 104

Reorder the terms:
-104 + 104 + 11x + x2 = 0 + 104

Combine like terms: -104 + 104 = 0
0 + 11x + x2 = 0 + 104
11x + x2 = 0 + 104

Combine like terms: 0 + 104 = 104
11x + x2 = 104

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 = 104 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 104 + 30.25

Combine like terms: 104 + 30.25 = 134.25
30.25 + 11x + x2 = 134.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 134.25

Calculate the square root of the right side: 11.586630226

Break this problem into two subproblems by setting 
(x + 5.5) equal to 11.586630226 and -11.586630226.

Subproblem 1

x + 5.5 = 11.586630226 Simplifying x + 5.5 = 11.586630226 Reorder the terms: 5.5 + x = 11.586630226 Solving 5.5 + x = 11.586630226 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 = 11.586630226 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 11.586630226 + -5.5 x = 11.586630226 + -5.5 Combine like terms: 11.586630226 + -5.5 = 6.086630226 x = 6.086630226 Simplifying x = 6.086630226

Subproblem 2

x + 5.5 = -11.586630226 Simplifying x + 5.5 = -11.586630226 Reorder the terms: 5.5 + x = -11.586630226 Solving 5.5 + x = -11.586630226 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 = -11.586630226 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -11.586630226 + -5.5 x = -11.586630226 + -5.5 Combine like terms: -11.586630226 + -5.5 = -17.086630226 x = -17.086630226 Simplifying x = -17.086630226

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.086630226, -17.086630226}

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