(x-2.8)(x+5.2)=0

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Solution for (x-2.8)(x+5.2)=0 equation: 


Simplifying
(x + -2.8)(x + 5.2) = 0

Reorder the terms:
(-2.8 + x)(x + 5.2) = 0

Reorder the terms:
(-2.8 + x)(5.2 + x) = 0

Multiply (-2.8 + x) * (5.2 + x)
(-2.8(5.2 + x) + x(5.2 + x)) = 0
((5.2 * -2.8 + x * -2.8) + x(5.2 + x)) = 0
((-14.56 + -2.8x) + x(5.2 + x)) = 0
(-14.56 + -2.8x + (5.2 * x + x * x)) = 0
(-14.56 + -2.8x + (5.2x + x2)) = 0

Combine like terms: -2.8x + 5.2x = 2.4x
(-14.56 + 2.4x + x2) = 0

Solving
-14.56 + 2.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '14.56' to each side of the equation.
-14.56 + 2.4x + 14.56 + x2 = 0 + 14.56

Reorder the terms:
-14.56 + 14.56 + 2.4x + x2 = 0 + 14.56

Combine like terms: -14.56 + 14.56 = 0.00
0.00 + 2.4x + x2 = 0 + 14.56
2.4x + x2 = 0 + 14.56

Combine like terms: 0 + 14.56 = 14.56
2.4x + x2 = 14.56

The x term is 2.4x.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4x + 1.44 + x2 = 14.56 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = 14.56 + 1.44

Combine like terms: 14.56 + 1.44 = 16
1.44 + 2.4x + x2 = 16

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(x + 1.2) equal to 4 and -4.


Subproblem 1
x + 1.2 = 4

Simplifying
x + 1.2 = 4

Reorder the terms:
1.2 + x = 4

Solving
1.2 + x = 4

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = 4 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = 4 + -1.2
x = 4 + -1.2

Combine like terms: 4 + -1.2 = 2.8
x = 2.8

Simplifying
x = 2.8


Subproblem 2
x + 1.2 = -4

Simplifying
x + 1.2 = -4

Reorder the terms:
1.2 + x = -4

Solving
1.2 + x = -4

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = -4 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = -4 + -1.2
x = -4 + -1.2

Combine like terms: -4 + -1.2 = -5.2
x = -5.2

Simplifying
x = -5.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.8, -5.2}

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