x^2+8.8x-72.5=0

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Solution for x^2+8.8x-72.5=0 equation: 


Simplifying
x2 + 8.8x + -72.5 = 0

Reorder the terms:
-72.5 + 8.8x + x2 = 0

Solving
-72.5 + 8.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '72.5' to each side of the equation.
-72.5 + 8.8x + 72.5 + x2 = 0 + 72.5

Reorder the terms:
-72.5 + 72.5 + 8.8x + x2 = 0 + 72.5

Combine like terms: -72.5 + 72.5 = 0.0
0.0 + 8.8x + x2 = 0 + 72.5
8.8x + x2 = 0 + 72.5

Combine like terms: 0 + 72.5 = 72.5
8.8x + x2 = 72.5

The x term is 8.8x.  Take half its coefficient (4.4).
Square it (19.36) and add it to both sides.

Add '19.36' to each side of the equation.
8.8x + 19.36 + x2 = 72.5 + 19.36

Reorder the terms:
19.36 + 8.8x + x2 = 72.5 + 19.36

Combine like terms: 72.5 + 19.36 = 91.86
19.36 + 8.8x + x2 = 91.86

Factor a perfect square on the left side:
(x + 4.4)(x + 4.4) = 91.86

Calculate the square root of the right side: 9.584362264

Break this problem into two subproblems by setting 
(x + 4.4) equal to 9.584362264 and -9.584362264.


Subproblem 1
x + 4.4 = 9.584362264

Simplifying
x + 4.4 = 9.584362264

Reorder the terms:
4.4 + x = 9.584362264

Solving
4.4 + x = 9.584362264

Solving for variable 'x'.

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

Add '-4.4' to each side of the equation.
4.4 + -4.4 + x = 9.584362264 + -4.4

Combine like terms: 4.4 + -4.4 = 0.0
0.0 + x = 9.584362264 + -4.4
x = 9.584362264 + -4.4

Combine like terms: 9.584362264 + -4.4 = 5.184362264
x = 5.184362264

Simplifying
x = 5.184362264


Subproblem 2
x + 4.4 = -9.584362264

Simplifying
x + 4.4 = -9.584362264

Reorder the terms:
4.4 + x = -9.584362264

Solving
4.4 + x = -9.584362264

Solving for variable 'x'.

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

Add '-4.4' to each side of the equation.
4.4 + -4.4 + x = -9.584362264 + -4.4

Combine like terms: 4.4 + -4.4 = 0.0
0.0 + x = -9.584362264 + -4.4
x = -9.584362264 + -4.4

Combine like terms: -9.584362264 + -4.4 = -13.984362264
x = -13.984362264

Simplifying
x = -13.984362264


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.184362264, -13.984362264}

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