x^2+4x-172.5=0

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Solution for x^2+4x-172.5=0 equation: 


Simplifying
x2 + 4x + -172.5 = 0

Reorder the terms:
-172.5 + 4x + x2 = 0

Solving
-172.5 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '172.5' to each side of the equation.
-172.5 + 4x + 172.5 + x2 = 0 + 172.5

Reorder the terms:
-172.5 + 172.5 + 4x + x2 = 0 + 172.5

Combine like terms: -172.5 + 172.5 = 0.0
0.0 + 4x + x2 = 0 + 172.5
4x + x2 = 0 + 172.5

Combine like terms: 0 + 172.5 = 172.5
4x + x2 = 172.5

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 172.5 + 4

Reorder the terms:
4 + 4x + x2 = 172.5 + 4

Combine like terms: 172.5 + 4 = 176.5
4 + 4x + x2 = 176.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 176.5

Calculate the square root of the right side: 13.285330256

Break this problem into two subproblems by setting 
(x + 2) equal to 13.285330256 and -13.285330256.


Subproblem 1
x + 2 = 13.285330256

Simplifying
x + 2 = 13.285330256

Reorder the terms:
2 + x = 13.285330256

Solving
2 + x = 13.285330256

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 13.285330256 + -2

Combine like terms: 2 + -2 = 0
0 + x = 13.285330256 + -2
x = 13.285330256 + -2

Combine like terms: 13.285330256 + -2 = 11.285330256
x = 11.285330256

Simplifying
x = 11.285330256


Subproblem 2
x + 2 = -13.285330256

Simplifying
x + 2 = -13.285330256

Reorder the terms:
2 + x = -13.285330256

Solving
2 + x = -13.285330256

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -13.285330256 + -2

Combine like terms: 2 + -2 = 0
0 + x = -13.285330256 + -2
x = -13.285330256 + -2

Combine like terms: -13.285330256 + -2 = -15.285330256
x = -15.285330256

Simplifying
x = -15.285330256


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.285330256, -15.285330256}

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