2(x^2+5x-540)=0

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Solution for 2(x^2+5x-540)=0 equation: 


Simplifying
2(x2 + 5x + -540) = 0

Reorder the terms:
2(-540 + 5x + x2) = 0
(-540 * 2 + 5x * 2 + x2 * 2) = 0
(-1080 + 10x + 2x2) = 0

Solving
-1080 + 10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-540 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-540 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-540 + 5x + x2 = 0

Solving
-540 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '540' to each side of the equation.
-540 + 5x + 540 + x2 = 0 + 540

Reorder the terms:
-540 + 540 + 5x + x2 = 0 + 540

Combine like terms: -540 + 540 = 0
0 + 5x + x2 = 0 + 540
5x + x2 = 0 + 540

Combine like terms: 0 + 540 = 540
5x + x2 = 540

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 540 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 540 + 6.25

Combine like terms: 540 + 6.25 = 546.25
6.25 + 5x + x2 = 546.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 546.25

Calculate the square root of the right side: 23.371991785

Break this problem into two subproblems by setting 
(x + 2.5) equal to 23.371991785 and -23.371991785.


Subproblem 1
x + 2.5 = 23.371991785

Simplifying
x + 2.5 = 23.371991785

Reorder the terms:
2.5 + x = 23.371991785

Solving
2.5 + x = 23.371991785

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 23.371991785 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 23.371991785 + -2.5
x = 23.371991785 + -2.5

Combine like terms: 23.371991785 + -2.5 = 20.871991785
x = 20.871991785

Simplifying
x = 20.871991785


Subproblem 2
x + 2.5 = -23.371991785

Simplifying
x + 2.5 = -23.371991785

Reorder the terms:
2.5 + x = -23.371991785

Solving
2.5 + x = -23.371991785

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -23.371991785 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -23.371991785 + -2.5
x = -23.371991785 + -2.5

Combine like terms: -23.371991785 + -2.5 = -25.871991785
x = -25.871991785

Simplifying
x = -25.871991785


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.871991785, -25.871991785}
Solution
x = {20.871991785, -25.871991785}

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