x^2-8.4x+4.2=0

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Solution for x^2-8.4x+4.2=0 equation: 


Simplifying
x2 + -8.4x + 4.2 = 0

Reorder the terms:
4.2 + -8.4x + x2 = 0

Solving
4.2 + -8.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4.2' to each side of the equation.
4.2 + -8.4x + -4.2 + x2 = 0 + -4.2

Reorder the terms:
4.2 + -4.2 + -8.4x + x2 = 0 + -4.2

Combine like terms: 4.2 + -4.2 = 0.0
0.0 + -8.4x + x2 = 0 + -4.2
-8.4x + x2 = 0 + -4.2

Combine like terms: 0 + -4.2 = -4.2
-8.4x + x2 = -4.2

The x term is -8.4x.  Take half its coefficient (-4.2).
Square it (17.64) and add it to both sides.

Add '17.64' to each side of the equation.
-8.4x + 17.64 + x2 = -4.2 + 17.64

Reorder the terms:
17.64 + -8.4x + x2 = -4.2 + 17.64

Combine like terms: -4.2 + 17.64 = 13.44
17.64 + -8.4x + x2 = 13.44

Factor a perfect square on the left side:
(x + -4.2)(x + -4.2) = 13.44

Calculate the square root of the right side: 3.666060556

Break this problem into two subproblems by setting 
(x + -4.2) equal to 3.666060556 and -3.666060556.


Subproblem 1
x + -4.2 = 3.666060556

Simplifying
x + -4.2 = 3.666060556

Reorder the terms:
-4.2 + x = 3.666060556

Solving
-4.2 + x = 3.666060556

Solving for variable 'x'.

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

Add '4.2' to each side of the equation.
-4.2 + 4.2 + x = 3.666060556 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + x = 3.666060556 + 4.2
x = 3.666060556 + 4.2

Combine like terms: 3.666060556 + 4.2 = 7.866060556
x = 7.866060556

Simplifying
x = 7.866060556


Subproblem 2
x + -4.2 = -3.666060556

Simplifying
x + -4.2 = -3.666060556

Reorder the terms:
-4.2 + x = -3.666060556

Solving
-4.2 + x = -3.666060556

Solving for variable 'x'.

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

Add '4.2' to each side of the equation.
-4.2 + 4.2 + x = -3.666060556 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + x = -3.666060556 + 4.2
x = -3.666060556 + 4.2

Combine like terms: -3.666060556 + 4.2 = 0.533939444
x = 0.533939444

Simplifying
x = 0.533939444


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.866060556, 0.533939444}

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