x^2+4.2x-44.59=0

Solution for x^2+4.2x-44.59=0 equation:

Simplifying
x2 + 4.2x + -44.59 = 0

Reorder the terms:
-44.59 + 4.2x + x2 = 0

Solving
-44.59 + 4.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '44.59' to each side of the equation.
-44.59 + 4.2x + 44.59 + x2 = 0 + 44.59

Reorder the terms:
-44.59 + 44.59 + 4.2x + x2 = 0 + 44.59

Combine like terms: -44.59 + 44.59 = 0.00
0.00 + 4.2x + x2 = 0 + 44.59
4.2x + x2 = 0 + 44.59

Combine like terms: 0 + 44.59 = 44.59
4.2x + x2 = 44.59

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 = 44.59 + 4.41

Reorder the terms:
4.41 + 4.2x + x2 = 44.59 + 4.41

Combine like terms: 44.59 + 4.41 = 49
4.41 + 4.2x + x2 = 49

Factor a perfect square on the left side:
(x + 2.1)(x + 2.1) = 49

Calculate the square root of the right side: 7

Break this problem into two subproblems by setting 
(x + 2.1) equal to 7 and -7.

Subproblem 1
x + 2.1 = 7

Simplifying
x + 2.1 = 7

Reorder the terms:
2.1 + x = 7

Solving
2.1 + x = 7

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 = 7 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = 7 + -2.1
x = 7 + -2.1

Combine like terms: 7 + -2.1 = 4.9
x = 4.9

Simplifying
x = 4.9

Subproblem 2
x + 2.1 = -7

Simplifying
x + 2.1 = -7

Reorder the terms:
2.1 + x = -7

Solving
2.1 + x = -7

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 = -7 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = -7 + -2.1
x = -7 + -2.1

Combine like terms: -7 + -2.1 = -9.1
x = -9.1

Simplifying
x = -9.1

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.9, -9.1}