11x+x^2=2.5

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Solution for 11x+x^2=2.5 equation:


Simplifying
11x + x2 = 2.5

Solving
11x + x2 = 2.5

Solving for variable 'x'.

Reorder the terms:
-2.5 + 11x + x2 = 2.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
-2.5 + 11x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 11x + 2.5 + x2 = 0.0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 11x + x2 = 0.0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 11x + x2 = 0.0 + 2.5
11x + x2 = 0.0 + 2.5

Combine like terms: 0.0 + 2.5 = 2.5
11x + x2 = 2.5

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 = 2.5 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 2.5 + 30.25

Combine like terms: 2.5 + 30.25 = 32.75
30.25 + 11x + x2 = 32.75

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 32.75

Calculate the square root of the right side: 5.722761571

Break this problem into two subproblems by setting 
(x + 5.5) equal to 5.722761571 and -5.722761571.

Subproblem 1

x + 5.5 = 5.722761571 Simplifying x + 5.5 = 5.722761571 Reorder the terms: 5.5 + x = 5.722761571 Solving 5.5 + x = 5.722761571 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 = 5.722761571 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 5.722761571 + -5.5 x = 5.722761571 + -5.5 Combine like terms: 5.722761571 + -5.5 = 0.222761571 x = 0.222761571 Simplifying x = 0.222761571

Subproblem 2

x + 5.5 = -5.722761571 Simplifying x + 5.5 = -5.722761571 Reorder the terms: 5.5 + x = -5.722761571 Solving 5.5 + x = -5.722761571 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 = -5.722761571 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -5.722761571 + -5.5 x = -5.722761571 + -5.5 Combine like terms: -5.722761571 + -5.5 = -11.222761571 x = -11.222761571 Simplifying x = -11.222761571

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.222761571, -11.222761571}

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