x^2+8.8x=16.64

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Solution for x^2+8.8x=16.64 equation: 


Simplifying
x2 + 8.8x = 16.64

Reorder the terms:
8.8x + x2 = 16.64

Solving
8.8x + x2 = 16.64

Solving for variable 'x'.

Reorder the terms:
-16.64 + 8.8x + x2 = 16.64 + -16.64

Combine like terms: 16.64 + -16.64 = 0.00
-16.64 + 8.8x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '16.64' to each side of the equation.
-16.64 + 8.8x + 16.64 + x2 = 0.00 + 16.64

Reorder the terms:
-16.64 + 16.64 + 8.8x + x2 = 0.00 + 16.64

Combine like terms: -16.64 + 16.64 = 0.00
0.00 + 8.8x + x2 = 0.00 + 16.64
8.8x + x2 = 0.00 + 16.64

Combine like terms: 0.00 + 16.64 = 16.64
8.8x + x2 = 16.64

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 = 16.64 + 19.36

Reorder the terms:
19.36 + 8.8x + x2 = 16.64 + 19.36

Combine like terms: 16.64 + 19.36 = 36
19.36 + 8.8x + x2 = 36

Factor a perfect square on the left side:
(x + 4.4)(x + 4.4) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(x + 4.4) equal to 6 and -6.


Subproblem 1
x + 4.4 = 6

Simplifying
x + 4.4 = 6

Reorder the terms:
4.4 + x = 6

Solving
4.4 + x = 6

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 = 6 + -4.4

Combine like terms: 4.4 + -4.4 = 0.0
0.0 + x = 6 + -4.4
x = 6 + -4.4

Combine like terms: 6 + -4.4 = 1.6
x = 1.6

Simplifying
x = 1.6


Subproblem 2
x + 4.4 = -6

Simplifying
x + 4.4 = -6

Reorder the terms:
4.4 + x = -6

Solving
4.4 + x = -6

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 = -6 + -4.4

Combine like terms: 4.4 + -4.4 = 0.0
0.0 + x = -6 + -4.4
x = -6 + -4.4

Combine like terms: -6 + -4.4 = -10.4
x = -10.4

Simplifying
x = -10.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6, -10.4}

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