2x^2+8x-4.2=0

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Solution for 2x^2+8x-4.2=0 equation: 


Simplifying
2x2 + 8x + -4.2 = 0

Reorder the terms:
-4.2 + 8x + 2x2 = 0

Solving
-4.2 + 8x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-2.1 + 4x + x2 = 0

Move the constant term to the right:

Add '2.1' to each side of the equation.
-2.1 + 4x + 2.1 + x2 = 0 + 2.1

Reorder the terms:
-2.1 + 2.1 + 4x + x2 = 0 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + 4x + x2 = 0 + 2.1
4x + x2 = 0 + 2.1

Combine like terms: 0 + 2.1 = 2.1
4x + x2 = 2.1

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 2.1 + 4

Reorder the terms:
4 + 4x + x2 = 2.1 + 4

Combine like terms: 2.1 + 4 = 6.1
4 + 4x + x2 = 6.1

Factor a perfect square on the left side:
(x + 2)(x + 2) = 6.1

Calculate the square root of the right side: 2.469817807

Break this problem into two subproblems by setting 
(x + 2) equal to 2.469817807 and -2.469817807.


Subproblem 1
x + 2 = 2.469817807

Simplifying
x + 2 = 2.469817807

Reorder the terms:
2 + x = 2.469817807

Solving
2 + x = 2.469817807

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.469817807 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.469817807 + -2
x = 2.469817807 + -2

Combine like terms: 2.469817807 + -2 = 0.469817807
x = 0.469817807

Simplifying
x = 0.469817807


Subproblem 2
x + 2 = -2.469817807

Simplifying
x + 2 = -2.469817807

Reorder the terms:
2 + x = -2.469817807

Solving
2 + x = -2.469817807

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.469817807 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.469817807 + -2
x = -2.469817807 + -2

Combine like terms: -2.469817807 + -2 = -4.469817807
x = -4.469817807

Simplifying
x = -4.469817807


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.469817807, -4.469817807}

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