(x-5.3)(x-5.3)=25

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Solution for (x-5.3)(x-5.3)=25 equation: 


Simplifying
(x + -5.3)(x + -5.3) = 25

Reorder the terms:
(-5.3 + x)(x + -5.3) = 25

Reorder the terms:
(-5.3 + x)(-5.3 + x) = 25

Multiply (-5.3 + x) * (-5.3 + x)
(-5.3(-5.3 + x) + x(-5.3 + x)) = 25
((-5.3 * -5.3 + x * -5.3) + x(-5.3 + x)) = 25
((28.09 + -5.3x) + x(-5.3 + x)) = 25
(28.09 + -5.3x + (-5.3 * x + x * x)) = 25
(28.09 + -5.3x + (-5.3x + x2)) = 25

Combine like terms: -5.3x + -5.3x = -10.6x
(28.09 + -10.6x + x2) = 25

Solving
28.09 + -10.6x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
28.09 + -25 + -10.6x + x2 = 25 + -25

Combine like terms: 28.09 + -25 = 3.09
3.09 + -10.6x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
3.09 + -10.6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3.09' to each side of the equation.
3.09 + -10.6x + -3.09 + x2 = 0 + -3.09

Reorder the terms:
3.09 + -3.09 + -10.6x + x2 = 0 + -3.09

Combine like terms: 3.09 + -3.09 = 0.00
0.00 + -10.6x + x2 = 0 + -3.09
-10.6x + x2 = 0 + -3.09

Combine like terms: 0 + -3.09 = -3.09
-10.6x + x2 = -3.09

The x term is -10.6x.  Take half its coefficient (-5.3).
Square it (28.09) and add it to both sides.

Add '28.09' to each side of the equation.
-10.6x + 28.09 + x2 = -3.09 + 28.09

Reorder the terms:
28.09 + -10.6x + x2 = -3.09 + 28.09

Combine like terms: -3.09 + 28.09 = 25
28.09 + -10.6x + x2 = 25

Factor a perfect square on the left side:
(x + -5.3)(x + -5.3) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + -5.3) equal to 5 and -5.


Subproblem 1
x + -5.3 = 5

Simplifying
x + -5.3 = 5

Reorder the terms:
-5.3 + x = 5

Solving
-5.3 + x = 5

Solving for variable 'x'.

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

Add '5.3' to each side of the equation.
-5.3 + 5.3 + x = 5 + 5.3

Combine like terms: -5.3 + 5.3 = 0.0
0.0 + x = 5 + 5.3
x = 5 + 5.3

Combine like terms: 5 + 5.3 = 10.3
x = 10.3

Simplifying
x = 10.3


Subproblem 2
x + -5.3 = -5

Simplifying
x + -5.3 = -5

Reorder the terms:
-5.3 + x = -5

Solving
-5.3 + x = -5

Solving for variable 'x'.

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

Add '5.3' to each side of the equation.
-5.3 + 5.3 + x = -5 + 5.3

Combine like terms: -5.3 + 5.3 = 0.0
0.0 + x = -5 + 5.3
x = -5 + 5.3

Combine like terms: -5 + 5.3 = 0.3
x = 0.3

Simplifying
x = 0.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.3, 0.3}

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