x^2-4.2x-10.8=0

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Solution for x^2-4.2x-10.8=0 equation: 


Simplifying
x2 + -4.2x + -10.8 = 0

Reorder the terms:
-10.8 + -4.2x + x2 = 0

Solving
-10.8 + -4.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '10.8' to each side of the equation.
-10.8 + -4.2x + 10.8 + x2 = 0 + 10.8

Reorder the terms:
-10.8 + 10.8 + -4.2x + x2 = 0 + 10.8

Combine like terms: -10.8 + 10.8 = 0.0
0.0 + -4.2x + x2 = 0 + 10.8
-4.2x + x2 = 0 + 10.8

Combine like terms: 0 + 10.8 = 10.8
-4.2x + x2 = 10.8

The x term is -4.2x.  Take half its coefficient (-2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
-4.2x + 4.41 + x2 = 10.8 + 4.41

Reorder the terms:
4.41 + -4.2x + x2 = 10.8 + 4.41

Combine like terms: 10.8 + 4.41 = 15.21
4.41 + -4.2x + x2 = 15.21

Factor a perfect square on the left side:
(x + -2.1)(x + -2.1) = 15.21

Calculate the square root of the right side: 3.9

Break this problem into two subproblems by setting 
(x + -2.1) equal to 3.9 and -3.9.


Subproblem 1
x + -2.1 = 3.9

Simplifying
x + -2.1 = 3.9

Reorder the terms:
-2.1 + x = 3.9

Solving
-2.1 + x = 3.9

Solving for variable 'x'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + x = 3.9 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + x = 3.9 + 2.1
x = 3.9 + 2.1

Combine like terms: 3.9 + 2.1 = 6
x = 6

Simplifying
x = 6


Subproblem 2
x + -2.1 = -3.9

Simplifying
x + -2.1 = -3.9

Reorder the terms:
-2.1 + x = -3.9

Solving
-2.1 + x = -3.9

Solving for variable 'x'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + x = -3.9 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + x = -3.9 + 2.1
x = -3.9 + 2.1

Combine like terms: -3.9 + 2.1 = -1.8
x = -1.8

Simplifying
x = -1.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6, -1.8}

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