x^2+11.91x=2083.67

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Solution for x^2+11.91x=2083.67 equation:


Simplifying
x2 + 11.91x = 2083.67

Reorder the terms:
11.91x + x2 = 2083.67

Solving
11.91x + x2 = 2083.67

Solving for variable 'x'.

Reorder the terms:
-2083.67 + 11.91x + x2 = 2083.67 + -2083.67

Combine like terms: 2083.67 + -2083.67 = 0.00
-2083.67 + 11.91x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '2083.67' to each side of the equation.
-2083.67 + 11.91x + 2083.67 + x2 = 0.00 + 2083.67

Reorder the terms:
-2083.67 + 2083.67 + 11.91x + x2 = 0.00 + 2083.67

Combine like terms: -2083.67 + 2083.67 = 0.00
0.00 + 11.91x + x2 = 0.00 + 2083.67
11.91x + x2 = 0.00 + 2083.67

Combine like terms: 0.00 + 2083.67 = 2083.67
11.91x + x2 = 2083.67

The x term is 11.91x.  Take half its coefficient (5.955).
Square it (35.462025) and add it to both sides.

Add '35.462025' to each side of the equation.
11.91x + 35.462025 + x2 = 2083.67 + 35.462025

Reorder the terms:
35.462025 + 11.91x + x2 = 2083.67 + 35.462025

Combine like terms: 2083.67 + 35.462025 = 2119.132025
35.462025 + 11.91x + x2 = 2119.132025

Factor a perfect square on the left side:
(x + 5.955)(x + 5.955) = 2119.132025

Calculate the square root of the right side: 46.034031162

Break this problem into two subproblems by setting 
(x + 5.955) equal to 46.034031162 and -46.034031162.


Subproblem 1
x + 5.955 = 46.034031162

Simplifying
x + 5.955 = 46.034031162

Reorder the terms:
5.955 + x = 46.034031162

Solving
5.955 + x = 46.034031162

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5.955' to each side of the equation.
5.955 + -5.955 + x = 46.034031162 + -5.955

Combine like terms: 5.955 + -5.955 = 0.000
0.000 + x = 46.034031162 + -5.955
x = 46.034031162 + -5.955

Combine like terms: 46.034031162 + -5.955 = 40.079031162
x = 40.079031162

Simplifying
x = 40.079031162


Subproblem 2
x + 5.955 = -46.034031162

Simplifying
x + 5.955 = -46.034031162

Reorder the terms:
5.955 + x = -46.034031162

Solving
5.955 + x = -46.034031162

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5.955' to each side of the equation.
5.955 + -5.955 + x = -46.034031162 + -5.955

Combine like terms: 5.955 + -5.955 = 0.000
0.000 + x = -46.034031162 + -5.955
x = -46.034031162 + -5.955

Combine like terms: -46.034031162 + -5.955 = -51.989031162
x = -51.989031162

Simplifying
x = -51.989031162


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {40.079031162, -51.989031162}

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