1.1x^2-0.88x=0.528

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Solution for 1.1x^2-0.88x=0.528 equation: 


Simplifying
1.1x2 + -0.88x = 0.528

Reorder the terms:
-0.88x + 1.1x2 = 0.528

Solving
-0.88x + 1.1x2 = 0.528

Solving for variable 'x'.

Reorder the terms:
-0.528 + -0.88x + 1.1x2 = 0.528 + -0.528

Combine like terms: 0.528 + -0.528 = 0.000
-0.528 + -0.88x + 1.1x2 = 0.000

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

Divide each side by '1.1'.
-0.48 + -0.8x + x2 = 0.00

Move the constant term to the right:

Add '0.48' to each side of the equation.
-0.48 + -0.8x + 0.48 + x2 = 0.00 + 0.48

Reorder the terms:
-0.48 + 0.48 + -0.8x + x2 = 0.00 + 0.48

Combine like terms: -0.48 + 0.48 = 0.00
0.00 + -0.8x + x2 = 0.00 + 0.48
-0.8x + x2 = 0.00 + 0.48

Combine like terms: 0.00 + 0.48 = 0.48
-0.8x + x2 = 0.48

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 0.48 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 0.48 + 0.16

Combine like terms: 0.48 + 0.16 = 0.64
0.16 + -0.8x + x2 = 0.64

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 0.64

Calculate the square root of the right side: 0.8

Break this problem into two subproblems by setting 
(x + -0.4) equal to 0.8 and -0.8.


Subproblem 1
x + -0.4 = 0.8

Simplifying
x + -0.4 = 0.8

Reorder the terms:
-0.4 + x = 0.8

Solving
-0.4 + x = 0.8

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = 0.8 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = 0.8 + 0.4
x = 0.8 + 0.4

Combine like terms: 0.8 + 0.4 = 1.2
x = 1.2

Simplifying
x = 1.2


Subproblem 2
x + -0.4 = -0.8

Simplifying
x + -0.4 = -0.8

Reorder the terms:
-0.4 + x = -0.8

Solving
-0.4 + x = -0.8

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = -0.8 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = -0.8 + 0.4
x = -0.8 + 0.4

Combine like terms: -0.8 + 0.4 = -0.4
x = -0.4

Simplifying
x = -0.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2, -0.4}

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