X^2+4.2X-0.57=0

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Solution for X^2+4.2X-0.57=0 equation: 


Simplifying
X2 + 4.2X + -0.57 = 0

Reorder the terms:
-0.57 + 4.2X + X2 = 0

Solving
-0.57 + 4.2X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '0.57' to each side of the equation.
-0.57 + 4.2X + 0.57 + X2 = 0 + 0.57

Reorder the terms:
-0.57 + 0.57 + 4.2X + X2 = 0 + 0.57

Combine like terms: -0.57 + 0.57 = 0.00
0.00 + 4.2X + X2 = 0 + 0.57
4.2X + X2 = 0 + 0.57

Combine like terms: 0 + 0.57 = 0.57
4.2X + X2 = 0.57

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 = 0.57 + 4.41

Reorder the terms:
4.41 + 4.2X + X2 = 0.57 + 4.41

Combine like terms: 0.57 + 4.41 = 4.98
4.41 + 4.2X + X2 = 4.98

Factor a perfect square on the left side:
(X + 2.1)(X + 2.1) = 4.98

Calculate the square root of the right side: 2.23159136

Break this problem into two subproblems by setting 
(X + 2.1) equal to 2.23159136 and -2.23159136.


Subproblem 1
X + 2.1 = 2.23159136

Simplifying
X + 2.1 = 2.23159136

Reorder the terms:
2.1 + X = 2.23159136

Solving
2.1 + X = 2.23159136

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 = 2.23159136 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + X = 2.23159136 + -2.1
X = 2.23159136 + -2.1

Combine like terms: 2.23159136 + -2.1 = 0.13159136
X = 0.13159136

Simplifying
X = 0.13159136


Subproblem 2
X + 2.1 = -2.23159136

Simplifying
X + 2.1 = -2.23159136

Reorder the terms:
2.1 + X = -2.23159136

Solving
2.1 + X = -2.23159136

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 = -2.23159136 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + X = -2.23159136 + -2.1
X = -2.23159136 + -2.1

Combine like terms: -2.23159136 + -2.1 = -4.33159136
X = -4.33159136

Simplifying
X = -4.33159136


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.13159136, -4.33159136}

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