x^2=11x-2.8

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Solution for x^2=11x-2.8 equation: 


Simplifying
x2 = 11x + -2.8

Reorder the terms:
x2 = -2.8 + 11x

Solving
x2 = -2.8 + 11x

Solving for variable 'x'.

Reorder the terms:
2.8 + -11x + x2 = -2.8 + 11x + 2.8 + -11x

Reorder the terms:
2.8 + -11x + x2 = -2.8 + 2.8 + 11x + -11x

Combine like terms: -2.8 + 2.8 = 0.0
2.8 + -11x + x2 = 0.0 + 11x + -11x
2.8 + -11x + x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
2.8 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2.8' to each side of the equation.
2.8 + -11x + -2.8 + x2 = 0 + -2.8

Reorder the terms:
2.8 + -2.8 + -11x + x2 = 0 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + -11x + x2 = 0 + -2.8
-11x + x2 = 0 + -2.8

Combine like terms: 0 + -2.8 = -2.8
-11x + x2 = -2.8

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 = -2.8 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -2.8 + 30.25

Combine like terms: -2.8 + 30.25 = 27.45
30.25 + -11x + x2 = 27.45

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 27.45

Calculate the square root of the right side: 5.239274759

Break this problem into two subproblems by setting 
(x + -5.5) equal to 5.239274759 and -5.239274759.


Subproblem 1
x + -5.5 = 5.239274759

Simplifying
x + -5.5 = 5.239274759

Reorder the terms:
-5.5 + x = 5.239274759

Solving
-5.5 + x = 5.239274759

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 = 5.239274759 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 5.239274759 + 5.5
x = 5.239274759 + 5.5

Combine like terms: 5.239274759 + 5.5 = 10.739274759
x = 10.739274759

Simplifying
x = 10.739274759


Subproblem 2
x + -5.5 = -5.239274759

Simplifying
x + -5.5 = -5.239274759

Reorder the terms:
-5.5 + x = -5.239274759

Solving
-5.5 + x = -5.239274759

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 = -5.239274759 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -5.239274759 + 5.5
x = -5.239274759 + 5.5

Combine like terms: -5.239274759 + 5.5 = 0.260725241
x = 0.260725241

Simplifying
x = 0.260725241


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.739274759, 0.260725241}

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