0=x^2+20x-540.24

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Solution for 0=x^2+20x-540.24 equation: 


Simplifying
0 = x2 + 20x + -540.24

Reorder the terms:
0 = -540.24 + 20x + x2

Solving
0 = -540.24 + 20x + x2

Solving for variable 'x'.

Combine like terms: 0 + 540.24 = 540.24
540.24 + -20x + -1x2 = -540.24 + 20x + x2 + 540.24 + -20x + -1x2

Reorder the terms:
540.24 + -20x + -1x2 = -540.24 + 540.24 + 20x + -20x + x2 + -1x2

Combine like terms: -540.24 + 540.24 = 0.00
540.24 + -20x + -1x2 = 0.00 + 20x + -20x + x2 + -1x2
540.24 + -20x + -1x2 = 20x + -20x + x2 + -1x2

Combine like terms: 20x + -20x = 0
540.24 + -20x + -1x2 = 0 + x2 + -1x2
540.24 + -20x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
540.24 + -20x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-540.24 + 20x + x2 = 0

Move the constant term to the right:

Add '540.24' to each side of the equation.
-540.24 + 20x + 540.24 + x2 = 0 + 540.24

Reorder the terms:
-540.24 + 540.24 + 20x + x2 = 0 + 540.24

Combine like terms: -540.24 + 540.24 = 0.00
0.00 + 20x + x2 = 0 + 540.24
20x + x2 = 0 + 540.24

Combine like terms: 0 + 540.24 = 540.24
20x + x2 = 540.24

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 540.24 + 100

Reorder the terms:
100 + 20x + x2 = 540.24 + 100

Combine like terms: 540.24 + 100 = 640.24
100 + 20x + x2 = 640.24

Factor a perfect square on the left side:
(x + 10)(x + 10) = 640.24

Calculate the square root of the right side: 25.302964253

Break this problem into two subproblems by setting 
(x + 10) equal to 25.302964253 and -25.302964253.


Subproblem 1
x + 10 = 25.302964253

Simplifying
x + 10 = 25.302964253

Reorder the terms:
10 + x = 25.302964253

Solving
10 + x = 25.302964253

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 25.302964253 + -10

Combine like terms: 10 + -10 = 0
0 + x = 25.302964253 + -10
x = 25.302964253 + -10

Combine like terms: 25.302964253 + -10 = 15.302964253
x = 15.302964253

Simplifying
x = 15.302964253


Subproblem 2
x + 10 = -25.302964253

Simplifying
x + 10 = -25.302964253

Reorder the terms:
10 + x = -25.302964253

Solving
10 + x = -25.302964253

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -25.302964253 + -10

Combine like terms: 10 + -10 = 0
0 + x = -25.302964253 + -10
x = -25.302964253 + -10

Combine like terms: -25.302964253 + -10 = -35.302964253
x = -35.302964253

Simplifying
x = -35.302964253


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.302964253, -35.302964253}

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