(x+12.9)x=723.1

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Solution for (x+12.9)x=723.1 equation: 


Simplifying
(x + 12.9) * x = 723.1

Reorder the terms:
(12.9 + x) * x = 723.1

Reorder the terms for easier multiplication:
x(12.9 + x) = 723.1
(12.9 * x + x * x) = 723.1
(12.9x + x2) = 723.1

Solving
12.9x + x2 = 723.1

Solving for variable 'x'.

Reorder the terms:
-723.1 + 12.9x + x2 = 723.1 + -723.1

Combine like terms: 723.1 + -723.1 = 0.0
-723.1 + 12.9x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '723.1' to each side of the equation.
-723.1 + 12.9x + 723.1 + x2 = 0.0 + 723.1

Reorder the terms:
-723.1 + 723.1 + 12.9x + x2 = 0.0 + 723.1

Combine like terms: -723.1 + 723.1 = 0.0
0.0 + 12.9x + x2 = 0.0 + 723.1
12.9x + x2 = 0.0 + 723.1

Combine like terms: 0.0 + 723.1 = 723.1
12.9x + x2 = 723.1

The x term is 12.9x.  Take half its coefficient (6.45).
Square it (41.6025) and add it to both sides.

Add '41.6025' to each side of the equation.
12.9x + 41.6025 + x2 = 723.1 + 41.6025

Reorder the terms:
41.6025 + 12.9x + x2 = 723.1 + 41.6025

Combine like terms: 723.1 + 41.6025 = 764.7025
41.6025 + 12.9x + x2 = 764.7025

Factor a perfect square on the left side:
(x + 6.45)(x + 6.45) = 764.7025

Calculate the square root of the right side: 27.653254781

Break this problem into two subproblems by setting 
(x + 6.45) equal to 27.653254781 and -27.653254781.


Subproblem 1
x + 6.45 = 27.653254781

Simplifying
x + 6.45 = 27.653254781

Reorder the terms:
6.45 + x = 27.653254781

Solving
6.45 + x = 27.653254781

Solving for variable 'x'.

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

Add '-6.45' to each side of the equation.
6.45 + -6.45 + x = 27.653254781 + -6.45

Combine like terms: 6.45 + -6.45 = 0.00
0.00 + x = 27.653254781 + -6.45
x = 27.653254781 + -6.45

Combine like terms: 27.653254781 + -6.45 = 21.203254781
x = 21.203254781

Simplifying
x = 21.203254781


Subproblem 2
x + 6.45 = -27.653254781

Simplifying
x + 6.45 = -27.653254781

Reorder the terms:
6.45 + x = -27.653254781

Solving
6.45 + x = -27.653254781

Solving for variable 'x'.

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

Add '-6.45' to each side of the equation.
6.45 + -6.45 + x = -27.653254781 + -6.45

Combine like terms: 6.45 + -6.45 = 0.00
0.00 + x = -27.653254781 + -6.45
x = -27.653254781 + -6.45

Combine like terms: -27.653254781 + -6.45 = -34.103254781
x = -34.103254781

Simplifying
x = -34.103254781


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.203254781, -34.103254781}

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