(x-2.8)(x-2.8)=39.69

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Solution for (x-2.8)(x-2.8)=39.69 equation: 


Simplifying
(x + -2.8)(x + -2.8) = 39.69

Reorder the terms:
(-2.8 + x)(x + -2.8) = 39.69

Reorder the terms:
(-2.8 + x)(-2.8 + x) = 39.69

Multiply (-2.8 + x) * (-2.8 + x)
(-2.8(-2.8 + x) + x(-2.8 + x)) = 39.69
((-2.8 * -2.8 + x * -2.8) + x(-2.8 + x)) = 39.69
((7.84 + -2.8x) + x(-2.8 + x)) = 39.69
(7.84 + -2.8x + (-2.8 * x + x * x)) = 39.69
(7.84 + -2.8x + (-2.8x + x2)) = 39.69

Combine like terms: -2.8x + -2.8x = -5.6x
(7.84 + -5.6x + x2) = 39.69

Solving
7.84 + -5.6x + x2 = 39.69

Solving for variable 'x'.

Reorder the terms:
7.84 + -39.69 + -5.6x + x2 = 39.69 + -39.69

Combine like terms: 7.84 + -39.69 = -31.85
-31.85 + -5.6x + x2 = 39.69 + -39.69

Combine like terms: 39.69 + -39.69 = 0.00
-31.85 + -5.6x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '31.85' to each side of the equation.
-31.85 + -5.6x + 31.85 + x2 = 0.00 + 31.85

Reorder the terms:
-31.85 + 31.85 + -5.6x + x2 = 0.00 + 31.85

Combine like terms: -31.85 + 31.85 = 0.00
0.00 + -5.6x + x2 = 0.00 + 31.85
-5.6x + x2 = 0.00 + 31.85

Combine like terms: 0.00 + 31.85 = 31.85
-5.6x + x2 = 31.85

The x term is -5.6x.  Take half its coefficient (-2.8).
Square it (7.84) and add it to both sides.

Add '7.84' to each side of the equation.
-5.6x + 7.84 + x2 = 31.85 + 7.84

Reorder the terms:
7.84 + -5.6x + x2 = 31.85 + 7.84

Combine like terms: 31.85 + 7.84 = 39.69
7.84 + -5.6x + x2 = 39.69

Factor a perfect square on the left side:
(x + -2.8)(x + -2.8) = 39.69

Calculate the square root of the right side: 6.3

Break this problem into two subproblems by setting 
(x + -2.8) equal to 6.3 and -6.3.


Subproblem 1
x + -2.8 = 6.3

Simplifying
x + -2.8 = 6.3

Reorder the terms:
-2.8 + x = 6.3

Solving
-2.8 + x = 6.3

Solving for variable 'x'.

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

Add '2.8' to each side of the equation.
-2.8 + 2.8 + x = 6.3 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + x = 6.3 + 2.8
x = 6.3 + 2.8

Combine like terms: 6.3 + 2.8 = 9.1
x = 9.1

Simplifying
x = 9.1


Subproblem 2
x + -2.8 = -6.3

Simplifying
x + -2.8 = -6.3

Reorder the terms:
-2.8 + x = -6.3

Solving
-2.8 + x = -6.3

Solving for variable 'x'.

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

Add '2.8' to each side of the equation.
-2.8 + 2.8 + x = -6.3 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + x = -6.3 + 2.8
x = -6.3 + 2.8

Combine like terms: -6.3 + 2.8 = -3.5
x = -3.5

Simplifying
x = -3.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.1, -3.5}

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