8.8x+x^2=72.25

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Solution for 8.8x+x^2=72.25 equation: 


Simplifying
8.8x + x2 = 72.25

Solving
8.8x + x2 = 72.25

Solving for variable 'x'.

Reorder the terms:
-72.25 + 8.8x + x2 = 72.25 + -72.25

Combine like terms: 72.25 + -72.25 = 0.00
-72.25 + 8.8x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '72.25' to each side of the equation.
-72.25 + 8.8x + 72.25 + x2 = 0.00 + 72.25

Reorder the terms:
-72.25 + 72.25 + 8.8x + x2 = 0.00 + 72.25

Combine like terms: -72.25 + 72.25 = 0.00
0.00 + 8.8x + x2 = 0.00 + 72.25
8.8x + x2 = 0.00 + 72.25

Combine like terms: 0.00 + 72.25 = 72.25
8.8x + x2 = 72.25

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 = 72.25 + 19.36

Reorder the terms:
19.36 + 8.8x + x2 = 72.25 + 19.36

Combine like terms: 72.25 + 19.36 = 91.61
19.36 + 8.8x + x2 = 91.61

Factor a perfect square on the left side:
(x + 4.4)(x + 4.4) = 91.61

Calculate the square root of the right side: 9.5713113

Break this problem into two subproblems by setting 
(x + 4.4) equal to 9.5713113 and -9.5713113.


Subproblem 1
x + 4.4 = 9.5713113

Simplifying
x + 4.4 = 9.5713113

Reorder the terms:
4.4 + x = 9.5713113

Solving
4.4 + x = 9.5713113

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 = 9.5713113 + -4.4

Combine like terms: 4.4 + -4.4 = 0.0
0.0 + x = 9.5713113 + -4.4
x = 9.5713113 + -4.4

Combine like terms: 9.5713113 + -4.4 = 5.1713113
x = 5.1713113

Simplifying
x = 5.1713113


Subproblem 2
x + 4.4 = -9.5713113

Simplifying
x + 4.4 = -9.5713113

Reorder the terms:
4.4 + x = -9.5713113

Solving
4.4 + x = -9.5713113

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 = -9.5713113 + -4.4

Combine like terms: 4.4 + -4.4 = 0.0
0.0 + x = -9.5713113 + -4.4
x = -9.5713113 + -4.4

Combine like terms: -9.5713113 + -4.4 = -13.9713113
x = -13.9713113

Simplifying
x = -13.9713113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.1713113, -13.9713113}

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