-0.9x(x-8)=1.1x+5.3

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Solution for -0.9x(x-8)=1.1x+5.3 equation:


Simplifying
-0.9x(x + -8) = 1.1x + 5.3

Reorder the terms:
-0.9x(-8 + x) = 1.1x + 5.3
(-8 * -0.9x + x * -0.9x) = 1.1x + 5.3
(7.2x + -0.9x2) = 1.1x + 5.3

Reorder the terms:
7.2x + -0.9x2 = 5.3 + 1.1x

Solving
7.2x + -0.9x2 = 5.3 + 1.1x

Solving for variable 'x'.

Reorder the terms:
-5.3 + 7.2x + -1.1x + -0.9x2 = 5.3 + 1.1x + -5.3 + -1.1x

Combine like terms: 7.2x + -1.1x = 6.1x
-5.3 + 6.1x + -0.9x2 = 5.3 + 1.1x + -5.3 + -1.1x

Reorder the terms:
-5.3 + 6.1x + -0.9x2 = 5.3 + -5.3 + 1.1x + -1.1x

Combine like terms: 5.3 + -5.3 = 0.0
-5.3 + 6.1x + -0.9x2 = 0.0 + 1.1x + -1.1x
-5.3 + 6.1x + -0.9x2 = 1.1x + -1.1x

Combine like terms: 1.1x + -1.1x = 0.0
-5.3 + 6.1x + -0.9x2 = 0.0

Begin completing the square.  Divide all terms by
-0.9 the coefficient of the squared term: 

Divide each side by '-0.9'.
5.888888889 + -6.777777778x + x2 = 0

Move the constant term to the right:

Add '-5.888888889' to each side of the equation.
5.888888889 + -6.777777778x + -5.888888889 + x2 = 0 + -5.888888889

Reorder the terms:
5.888888889 + -5.888888889 + -6.777777778x + x2 = 0 + -5.888888889

Combine like terms: 5.888888889 + -5.888888889 = 0.000000000
0.000000000 + -6.777777778x + x2 = 0 + -5.888888889
-6.777777778x + x2 = 0 + -5.888888889

Combine like terms: 0 + -5.888888889 = -5.888888889
-6.777777778x + x2 = -5.888888889

The x term is -6.777777778x.  Take half its coefficient (-3.388888889).
Square it (11.48456790) and add it to both sides.

Add '11.48456790' to each side of the equation.
-6.777777778x + 11.48456790 + x2 = -5.888888889 + 11.48456790

Reorder the terms:
11.48456790 + -6.777777778x + x2 = -5.888888889 + 11.48456790

Combine like terms: -5.888888889 + 11.48456790 = 5.595679011
11.48456790 + -6.777777778x + x2 = 5.595679011

Factor a perfect square on the left side:
(x + -3.388888889)(x + -3.388888889) = 5.595679011

Calculate the square root of the right side: 2.365518761

Break this problem into two subproblems by setting 
(x + -3.388888889) equal to 2.365518761 and -2.365518761.

Subproblem 1

x + -3.388888889 = 2.365518761 Simplifying x + -3.388888889 = 2.365518761 Reorder the terms: -3.388888889 + x = 2.365518761 Solving -3.388888889 + x = 2.365518761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.388888889' to each side of the equation. -3.388888889 + 3.388888889 + x = 2.365518761 + 3.388888889 Combine like terms: -3.388888889 + 3.388888889 = 0.000000000 0.000000000 + x = 2.365518761 + 3.388888889 x = 2.365518761 + 3.388888889 Combine like terms: 2.365518761 + 3.388888889 = 5.75440765 x = 5.75440765 Simplifying x = 5.75440765

Subproblem 2

x + -3.388888889 = -2.365518761 Simplifying x + -3.388888889 = -2.365518761 Reorder the terms: -3.388888889 + x = -2.365518761 Solving -3.388888889 + x = -2.365518761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.388888889' to each side of the equation. -3.388888889 + 3.388888889 + x = -2.365518761 + 3.388888889 Combine like terms: -3.388888889 + 3.388888889 = 0.000000000 0.000000000 + x = -2.365518761 + 3.388888889 x = -2.365518761 + 3.388888889 Combine like terms: -2.365518761 + 3.388888889 = 1.023370128 x = 1.023370128 Simplifying x = 1.023370128

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.75440765, 1.023370128}

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