(x+4.45)(x+4.45)=12.25

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Solution for (x+4.45)(x+4.45)=12.25 equation: 


Simplifying
(x + 4.45)(x + 4.45) = 12.25

Reorder the terms:
(4.45 + x)(x + 4.45) = 12.25

Reorder the terms:
(4.45 + x)(4.45 + x) = 12.25

Multiply (4.45 + x) * (4.45 + x)
(4.45(4.45 + x) + x(4.45 + x)) = 12.25
((4.45 * 4.45 + x * 4.45) + x(4.45 + x)) = 12.25
((19.8025 + 4.45x) + x(4.45 + x)) = 12.25
(19.8025 + 4.45x + (4.45 * x + x * x)) = 12.25
(19.8025 + 4.45x + (4.45x + x2)) = 12.25

Combine like terms: 4.45x + 4.45x = 8.9x
(19.8025 + 8.9x + x2) = 12.25

Solving
19.8025 + 8.9x + x2 = 12.25

Solving for variable 'x'.

Reorder the terms:
19.8025 + -12.25 + 8.9x + x2 = 12.25 + -12.25

Combine like terms: 19.8025 + -12.25 = 7.5525
7.5525 + 8.9x + x2 = 12.25 + -12.25

Combine like terms: 12.25 + -12.25 = 0.00
7.5525 + 8.9x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-7.5525' to each side of the equation.
7.5525 + 8.9x + -7.5525 + x2 = 0.00 + -7.5525

Reorder the terms:
7.5525 + -7.5525 + 8.9x + x2 = 0.00 + -7.5525

Combine like terms: 7.5525 + -7.5525 = 0.0000
0.0000 + 8.9x + x2 = 0.00 + -7.5525
8.9x + x2 = 0.00 + -7.5525

Combine like terms: 0.00 + -7.5525 = -7.5525
8.9x + x2 = -7.5525

The x term is 8.9x.  Take half its coefficient (4.45).
Square it (19.8025) and add it to both sides.

Add '19.8025' to each side of the equation.
8.9x + 19.8025 + x2 = -7.5525 + 19.8025

Reorder the terms:
19.8025 + 8.9x + x2 = -7.5525 + 19.8025

Combine like terms: -7.5525 + 19.8025 = 12.25
19.8025 + 8.9x + x2 = 12.25

Factor a perfect square on the left side:
(x + 4.45)(x + 4.45) = 12.25

Calculate the square root of the right side: 3.5

Break this problem into two subproblems by setting 
(x + 4.45) equal to 3.5 and -3.5.


Subproblem 1
x + 4.45 = 3.5

Simplifying
x + 4.45 = 3.5

Reorder the terms:
4.45 + x = 3.5

Solving
4.45 + x = 3.5

Solving for variable 'x'.

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

Add '-4.45' to each side of the equation.
4.45 + -4.45 + x = 3.5 + -4.45

Combine like terms: 4.45 + -4.45 = 0.00
0.00 + x = 3.5 + -4.45
x = 3.5 + -4.45

Combine like terms: 3.5 + -4.45 = -0.95
x = -0.95

Simplifying
x = -0.95


Subproblem 2
x + 4.45 = -3.5

Simplifying
x + 4.45 = -3.5

Reorder the terms:
4.45 + x = -3.5

Solving
4.45 + x = -3.5

Solving for variable 'x'.

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

Add '-4.45' to each side of the equation.
4.45 + -4.45 + x = -3.5 + -4.45

Combine like terms: 4.45 + -4.45 = 0.00
0.00 + x = -3.5 + -4.45
x = -3.5 + -4.45

Combine like terms: -3.5 + -4.45 = -7.95
x = -7.95

Simplifying
x = -7.95


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.95, -7.95}

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