(x+4.2)(x)=24.5

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


Simplifying
(x + 4.2)(x) = 24.5

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

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

Solving
4.2x + x2 = 24.5

Solving for variable 'x'.

Reorder the terms:
-24.5 + 4.2x + x2 = 24.5 + -24.5

Combine like terms: 24.5 + -24.5 = 0.0
-24.5 + 4.2x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '24.5' to each side of the equation.
-24.5 + 4.2x + 24.5 + x2 = 0.0 + 24.5

Reorder the terms:
-24.5 + 24.5 + 4.2x + x2 = 0.0 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + 4.2x + x2 = 0.0 + 24.5
4.2x + x2 = 0.0 + 24.5

Combine like terms: 0.0 + 24.5 = 24.5
4.2x + x2 = 24.5

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 = 24.5 + 4.41

Reorder the terms:
4.41 + 4.2x + x2 = 24.5 + 4.41

Combine like terms: 24.5 + 4.41 = 28.91
4.41 + 4.2x + x2 = 28.91

Factor a perfect square on the left side:
(x + 2.1)(x + 2.1) = 28.91

Calculate the square root of the right side: 5.376802024

Break this problem into two subproblems by setting 
(x + 2.1) equal to 5.376802024 and -5.376802024.


Subproblem 1
x + 2.1 = 5.376802024

Simplifying
x + 2.1 = 5.376802024

Reorder the terms:
2.1 + x = 5.376802024

Solving
2.1 + x = 5.376802024

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 = 5.376802024 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = 5.376802024 + -2.1
x = 5.376802024 + -2.1

Combine like terms: 5.376802024 + -2.1 = 3.276802024
x = 3.276802024

Simplifying
x = 3.276802024


Subproblem 2
x + 2.1 = -5.376802024

Simplifying
x + 2.1 = -5.376802024

Reorder the terms:
2.1 + x = -5.376802024

Solving
2.1 + x = -5.376802024

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 = -5.376802024 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = -5.376802024 + -2.1
x = -5.376802024 + -2.1

Combine like terms: -5.376802024 + -2.1 = -7.476802024
x = -7.476802024

Simplifying
x = -7.476802024


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.276802024, -7.476802024}

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