(x+4.2)(2x)=24.5

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Solution for (x+4.2)(2x)=24.5 equation: 


Simplifying
(x + 4.2)(2x) = 24.5

Reorder the terms:
(4.2 + x)(2x) = 24.5

Remove parenthesis around (2x)
(4.2 + x) * 2x = 24.5

Reorder the terms for easier multiplication:
2x(4.2 + x) = 24.5
(4.2 * 2x + x * 2x) = 24.5
(8.4x + 2x2) = 24.5

Solving
8.4x + 2x2 = 24.5

Solving for variable 'x'.

Reorder the terms:
-24.5 + 8.4x + 2x2 = 24.5 + -24.5

Combine like terms: 24.5 + -24.5 = 0.0
-24.5 + 8.4x + 2x2 = 0.0

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

Divide each side by '2'.
-12.25 + 4.2x + x2 = 0.0

Move the constant term to the right:

Add '12.25' to each side of the equation.
-12.25 + 4.2x + 12.25 + x2 = 0.0 + 12.25

Reorder the terms:
-12.25 + 12.25 + 4.2x + x2 = 0.0 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + 4.2x + x2 = 0.0 + 12.25
4.2x + x2 = 0.0 + 12.25

Combine like terms: 0.0 + 12.25 = 12.25
4.2x + x2 = 12.25

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 = 12.25 + 4.41

Reorder the terms:
4.41 + 4.2x + x2 = 12.25 + 4.41

Combine like terms: 12.25 + 4.41 = 16.66
4.41 + 4.2x + x2 = 16.66

Factor a perfect square on the left side:
(x + 2.1)(x + 2.1) = 16.66

Calculate the square root of the right side: 4.081666326

Break this problem into two subproblems by setting 
(x + 2.1) equal to 4.081666326 and -4.081666326.


Subproblem 1
x + 2.1 = 4.081666326

Simplifying
x + 2.1 = 4.081666326

Reorder the terms:
2.1 + x = 4.081666326

Solving
2.1 + x = 4.081666326

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 = 4.081666326 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = 4.081666326 + -2.1
x = 4.081666326 + -2.1

Combine like terms: 4.081666326 + -2.1 = 1.981666326
x = 1.981666326

Simplifying
x = 1.981666326


Subproblem 2
x + 2.1 = -4.081666326

Simplifying
x + 2.1 = -4.081666326

Reorder the terms:
2.1 + x = -4.081666326

Solving
2.1 + x = -4.081666326

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 = -4.081666326 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = -4.081666326 + -2.1
x = -4.081666326 + -2.1

Combine like terms: -4.081666326 + -2.1 = -6.181666326
x = -6.181666326

Simplifying
x = -6.181666326


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.981666326, -6.181666326}

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