x^2+540x-2=0

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Solution for x^2+540x-2=0 equation: 


Simplifying
x2 + 540x + -2 = 0

Reorder the terms:
-2 + 540x + x2 = 0

Solving
-2 + 540x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 540x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 540x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 540x + x2 = 0 + 2
540x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
540x + x2 = 2

The x term is 540x.  Take half its coefficient (270).
Square it (72900) and add it to both sides.

Add '72900' to each side of the equation.
540x + 72900 + x2 = 2 + 72900

Reorder the terms:
72900 + 540x + x2 = 2 + 72900

Combine like terms: 2 + 72900 = 72902
72900 + 540x + x2 = 72902

Factor a perfect square on the left side:
(x + 270)(x + 270) = 72902

Calculate the square root of the right side: 270.003703678

Break this problem into two subproblems by setting 
(x + 270) equal to 270.003703678 and -270.003703678.


Subproblem 1
x + 270 = 270.003703678

Simplifying
x + 270 = 270.003703678

Reorder the terms:
270 + x = 270.003703678

Solving
270 + x = 270.003703678

Solving for variable 'x'.

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

Add '-270' to each side of the equation.
270 + -270 + x = 270.003703678 + -270

Combine like terms: 270 + -270 = 0
0 + x = 270.003703678 + -270
x = 270.003703678 + -270

Combine like terms: 270.003703678 + -270 = 0.003703678
x = 0.003703678

Simplifying
x = 0.003703678


Subproblem 2
x + 270 = -270.003703678

Simplifying
x + 270 = -270.003703678

Reorder the terms:
270 + x = -270.003703678

Solving
270 + x = -270.003703678

Solving for variable 'x'.

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

Add '-270' to each side of the equation.
270 + -270 + x = -270.003703678 + -270

Combine like terms: 270 + -270 = 0
0 + x = -270.003703678 + -270
x = -270.003703678 + -270

Combine like terms: -270.003703678 + -270 = -540.003703678
x = -540.003703678

Simplifying
x = -540.003703678


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.003703678, -540.003703678}

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