x^2-13.6x=46.24

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Solution for x^2-13.6x=46.24 equation: 


Simplifying
x2 + -13.6x = 46.24

Reorder the terms:
-13.6x + x2 = 46.24

Solving
-13.6x + x2 = 46.24

Solving for variable 'x'.

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

Combine like terms: 46.24 + -46.24 = 0.00
-46.24 + -13.6x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '46.24' to each side of the equation.
-46.24 + -13.6x + 46.24 + x2 = 0.00 + 46.24

Reorder the terms:
-46.24 + 46.24 + -13.6x + x2 = 0.00 + 46.24

Combine like terms: -46.24 + 46.24 = 0.00
0.00 + -13.6x + x2 = 0.00 + 46.24
-13.6x + x2 = 0.00 + 46.24

Combine like terms: 0.00 + 46.24 = 46.24
-13.6x + x2 = 46.24

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 = 46.24 + 46.24

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

Combine like terms: 46.24 + 46.24 = 92.48
46.24 + -13.6x + x2 = 92.48

Factor a perfect square on the left side:
(x + -6.8)(x + -6.8) = 92.48

Calculate the square root of the right side: 9.616652224

Break this problem into two subproblems by setting 
(x + -6.8) equal to 9.616652224 and -9.616652224.


Subproblem 1
x + -6.8 = 9.616652224

Simplifying
x + -6.8 = 9.616652224

Reorder the terms:
-6.8 + x = 9.616652224

Solving
-6.8 + x = 9.616652224

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 = 9.616652224 + 6.8

Combine like terms: -6.8 + 6.8 = 0.0
0.0 + x = 9.616652224 + 6.8
x = 9.616652224 + 6.8

Combine like terms: 9.616652224 + 6.8 = 16.416652224
x = 16.416652224

Simplifying
x = 16.416652224


Subproblem 2
x + -6.8 = -9.616652224

Simplifying
x + -6.8 = -9.616652224

Reorder the terms:
-6.8 + x = -9.616652224

Solving
-6.8 + x = -9.616652224

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 = -9.616652224 + 6.8

Combine like terms: -6.8 + 6.8 = 0.0
0.0 + x = -9.616652224 + 6.8
x = -9.616652224 + 6.8

Combine like terms: -9.616652224 + 6.8 = -2.816652224
x = -2.816652224

Simplifying
x = -2.816652224


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.416652224, -2.816652224}

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