1.1x+.2x^2-5.5=0

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Solution for 1.1x+.2x^2-5.5=0 equation:


Simplifying
1.1x + 0.2x2 + -5.5 = 0

Reorder the terms:
-5.5 + 1.1x + 0.2x2 = 0

Solving
-5.5 + 1.1x + 0.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.2 the coefficient of the squared term: 

Divide each side by '0.2'.
-27.5 + 5.5x + x2 = 0

Move the constant term to the right:

Add '27.5' to each side of the equation.
-27.5 + 5.5x + 27.5 + x2 = 0 + 27.5

Reorder the terms:
-27.5 + 27.5 + 5.5x + x2 = 0 + 27.5

Combine like terms: -27.5 + 27.5 = 0.0
0.0 + 5.5x + x2 = 0 + 27.5
5.5x + x2 = 0 + 27.5

Combine like terms: 0 + 27.5 = 27.5
5.5x + x2 = 27.5

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = 27.5 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 27.5 + 7.5625

Combine like terms: 27.5 + 7.5625 = 35.0625
7.5625 + 5.5x + x2 = 35.0625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 35.0625

Calculate the square root of the right side: 5.921359641

Break this problem into two subproblems by setting 
(x + 2.75) equal to 5.921359641 and -5.921359641.

Subproblem 1

x + 2.75 = 5.921359641 Simplifying x + 2.75 = 5.921359641 Reorder the terms: 2.75 + x = 5.921359641 Solving 2.75 + x = 5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 5.921359641 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 5.921359641 + -2.75 x = 5.921359641 + -2.75 Combine like terms: 5.921359641 + -2.75 = 3.171359641 x = 3.171359641 Simplifying x = 3.171359641

Subproblem 2

x + 2.75 = -5.921359641 Simplifying x + 2.75 = -5.921359641 Reorder the terms: 2.75 + x = -5.921359641 Solving 2.75 + x = -5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -5.921359641 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -5.921359641 + -2.75 x = -5.921359641 + -2.75 Combine like terms: -5.921359641 + -2.75 = -8.671359641 x = -8.671359641 Simplifying x = -8.671359641

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.171359641, -8.671359641}

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