(x+1.3)(x+1.3)=20.25

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Solution for (x+1.3)(x+1.3)=20.25 equation: 


Simplifying
(x + 1.3)(x + 1.3) = 20.25

Reorder the terms:
(1.3 + x)(x + 1.3) = 20.25

Reorder the terms:
(1.3 + x)(1.3 + x) = 20.25

Multiply (1.3 + x) * (1.3 + x)
(1.3(1.3 + x) + x(1.3 + x)) = 20.25
((1.3 * 1.3 + x * 1.3) + x(1.3 + x)) = 20.25
((1.69 + 1.3x) + x(1.3 + x)) = 20.25
(1.69 + 1.3x + (1.3 * x + x * x)) = 20.25
(1.69 + 1.3x + (1.3x + x2)) = 20.25

Combine like terms: 1.3x + 1.3x = 2.6x
(1.69 + 2.6x + x2) = 20.25

Solving
1.69 + 2.6x + x2 = 20.25

Solving for variable 'x'.

Reorder the terms:
1.69 + -20.25 + 2.6x + x2 = 20.25 + -20.25

Combine like terms: 1.69 + -20.25 = -18.56
-18.56 + 2.6x + x2 = 20.25 + -20.25

Combine like terms: 20.25 + -20.25 = 0.00
-18.56 + 2.6x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '18.56' to each side of the equation.
-18.56 + 2.6x + 18.56 + x2 = 0.00 + 18.56

Reorder the terms:
-18.56 + 18.56 + 2.6x + x2 = 0.00 + 18.56

Combine like terms: -18.56 + 18.56 = 0.00
0.00 + 2.6x + x2 = 0.00 + 18.56
2.6x + x2 = 0.00 + 18.56

Combine like terms: 0.00 + 18.56 = 18.56
2.6x + x2 = 18.56

The x term is 2.6x.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6x + 1.69 + x2 = 18.56 + 1.69

Reorder the terms:
1.69 + 2.6x + x2 = 18.56 + 1.69

Combine like terms: 18.56 + 1.69 = 20.25
1.69 + 2.6x + x2 = 20.25

Factor a perfect square on the left side:
(x + 1.3)(x + 1.3) = 20.25

Calculate the square root of the right side: 4.5

Break this problem into two subproblems by setting 
(x + 1.3) equal to 4.5 and -4.5.


Subproblem 1
x + 1.3 = 4.5

Simplifying
x + 1.3 = 4.5

Reorder the terms:
1.3 + x = 4.5

Solving
1.3 + x = 4.5

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = 4.5 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = 4.5 + -1.3
x = 4.5 + -1.3

Combine like terms: 4.5 + -1.3 = 3.2
x = 3.2

Simplifying
x = 3.2


Subproblem 2
x + 1.3 = -4.5

Simplifying
x + 1.3 = -4.5

Reorder the terms:
1.3 + x = -4.5

Solving
1.3 + x = -4.5

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = -4.5 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = -4.5 + -1.3
x = -4.5 + -1.3

Combine like terms: -4.5 + -1.3 = -5.8
x = -5.8

Simplifying
x = -5.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.2, -5.8}

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