0=x^2-2.8x-4.8

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Solution for 0=x^2-2.8x-4.8 equation: 


Simplifying
0 = x2 + -2.8x + -4.8

Reorder the terms:
0 = -4.8 + -2.8x + x2

Solving
0 = -4.8 + -2.8x + x2

Solving for variable 'x'.

Combine like terms: 0 + 4.8 = 4.8
4.8 + 2.8x + -1x2 = -4.8 + -2.8x + x2 + 4.8 + 2.8x + -1x2

Reorder the terms:
4.8 + 2.8x + -1x2 = -4.8 + 4.8 + -2.8x + 2.8x + x2 + -1x2

Combine like terms: -4.8 + 4.8 = 0.0
4.8 + 2.8x + -1x2 = 0.0 + -2.8x + 2.8x + x2 + -1x2
4.8 + 2.8x + -1x2 = -2.8x + 2.8x + x2 + -1x2

Combine like terms: -2.8x + 2.8x = 0.0
4.8 + 2.8x + -1x2 = 0.0 + x2 + -1x2
4.8 + 2.8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4.8 + 2.8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4.8 + -2.8x + x2 = 0

Move the constant term to the right:

Add '4.8' to each side of the equation.
-4.8 + -2.8x + 4.8 + x2 = 0 + 4.8

Reorder the terms:
-4.8 + 4.8 + -2.8x + x2 = 0 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + -2.8x + x2 = 0 + 4.8
-2.8x + x2 = 0 + 4.8

Combine like terms: 0 + 4.8 = 4.8
-2.8x + x2 = 4.8

The x term is -2.8x.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8x + 1.96 + x2 = 4.8 + 1.96

Reorder the terms:
1.96 + -2.8x + x2 = 4.8 + 1.96

Combine like terms: 4.8 + 1.96 = 6.76
1.96 + -2.8x + x2 = 6.76

Factor a perfect square on the left side:
(x + -1.4)(x + -1.4) = 6.76

Calculate the square root of the right side: 2.6

Break this problem into two subproblems by setting 
(x + -1.4) equal to 2.6 and -2.6.


Subproblem 1
x + -1.4 = 2.6

Simplifying
x + -1.4 = 2.6

Reorder the terms:
-1.4 + x = 2.6

Solving
-1.4 + x = 2.6

Solving for variable 'x'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + x = 2.6 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = 2.6 + 1.4
x = 2.6 + 1.4

Combine like terms: 2.6 + 1.4 = 4
x = 4

Simplifying
x = 4


Subproblem 2
x + -1.4 = -2.6

Simplifying
x + -1.4 = -2.6

Reorder the terms:
-1.4 + x = -2.6

Solving
-1.4 + x = -2.6

Solving for variable 'x'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + x = -2.6 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = -2.6 + 1.4
x = -2.6 + 1.4

Combine like terms: -2.6 + 1.4 = -1.2
x = -1.2

Simplifying
x = -1.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4, -1.2}

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