x^2+13.6x=53.76

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Solution for x^2+13.6x=53.76 equation: 


Simplifying
x2 + 13.6x = 53.76

Reorder the terms:
13.6x + x2 = 53.76

Solving
13.6x + x2 = 53.76

Solving for variable 'x'.

Reorder the terms:
-53.76 + 13.6x + x2 = 53.76 + -53.76

Combine like terms: 53.76 + -53.76 = 0.00
-53.76 + 13.6x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '53.76' to each side of the equation.
-53.76 + 13.6x + 53.76 + x2 = 0.00 + 53.76

Reorder the terms:
-53.76 + 53.76 + 13.6x + x2 = 0.00 + 53.76

Combine like terms: -53.76 + 53.76 = 0.00
0.00 + 13.6x + x2 = 0.00 + 53.76
13.6x + x2 = 0.00 + 53.76

Combine like terms: 0.00 + 53.76 = 53.76
13.6x + x2 = 53.76

The x term is 13.6x.  Take half its coefficient (6.8).
Square it (46.24) and add it to both sides.

Add '46.24' to each side of the equation.
13.6x + 46.24 + x2 = 53.76 + 46.24

Reorder the terms:
46.24 + 13.6x + x2 = 53.76 + 46.24

Combine like terms: 53.76 + 46.24 = 100
46.24 + 13.6x + x2 = 100

Factor a perfect square on the left side:
(x + 6.8)(x + 6.8) = 100

Calculate the square root of the right side: 10

Break this problem into two subproblems by setting 
(x + 6.8) equal to 10 and -10.


Subproblem 1
x + 6.8 = 10

Simplifying
x + 6.8 = 10

Reorder the terms:
6.8 + x = 10

Solving
6.8 + x = 10

Solving for variable 'x'.

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

Add '-6.8' to each side of the equation.
6.8 + -6.8 + x = 10 + -6.8

Combine like terms: 6.8 + -6.8 = 0.0
0.0 + x = 10 + -6.8
x = 10 + -6.8

Combine like terms: 10 + -6.8 = 3.2
x = 3.2

Simplifying
x = 3.2


Subproblem 2
x + 6.8 = -10

Simplifying
x + 6.8 = -10

Reorder the terms:
6.8 + x = -10

Solving
6.8 + x = -10

Solving for variable 'x'.

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

Add '-6.8' to each side of the equation.
6.8 + -6.8 + x = -10 + -6.8

Combine like terms: 6.8 + -6.8 = 0.0
0.0 + x = -10 + -6.8
x = -10 + -6.8

Combine like terms: -10 + -6.8 = -16.8
x = -16.8

Simplifying
x = -16.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.2, -16.8}

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