(26-5x)(26-5x)=130

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Solution for (26-5x)(26-5x)=130 equation: 


Simplifying
(26 + -5x)(26 + -5x) = 130

Multiply (26 + -5x) * (26 + -5x)
(26(26 + -5x) + -5x * (26 + -5x)) = 130
((26 * 26 + -5x * 26) + -5x * (26 + -5x)) = 130
((676 + -130x) + -5x * (26 + -5x)) = 130
(676 + -130x + (26 * -5x + -5x * -5x)) = 130
(676 + -130x + (-130x + 25x2)) = 130

Combine like terms: -130x + -130x = -260x
(676 + -260x + 25x2) = 130

Solving
676 + -260x + 25x2 = 130

Solving for variable 'x'.

Reorder the terms:
676 + -130 + -260x + 25x2 = 130 + -130

Combine like terms: 676 + -130 = 546
546 + -260x + 25x2 = 130 + -130

Combine like terms: 130 + -130 = 0
546 + -260x + 25x2 = 0

Begin completing the square.  Divide all terms by
25 the coefficient of the squared term: 

Divide each side by '25'.
21.84 + -10.4x + x2 = 0

Move the constant term to the right:

Add '-21.84' to each side of the equation.
21.84 + -10.4x + -21.84 + x2 = 0 + -21.84

Reorder the terms:
21.84 + -21.84 + -10.4x + x2 = 0 + -21.84

Combine like terms: 21.84 + -21.84 = 0.00
0.00 + -10.4x + x2 = 0 + -21.84
-10.4x + x2 = 0 + -21.84

Combine like terms: 0 + -21.84 = -21.84
-10.4x + x2 = -21.84

The x term is -10.4x.  Take half its coefficient (-5.2).
Square it (27.04) and add it to both sides.

Add '27.04' to each side of the equation.
-10.4x + 27.04 + x2 = -21.84 + 27.04

Reorder the terms:
27.04 + -10.4x + x2 = -21.84 + 27.04

Combine like terms: -21.84 + 27.04 = 5.2
27.04 + -10.4x + x2 = 5.2

Factor a perfect square on the left side:
(x + -5.2)(x + -5.2) = 5.2

Calculate the square root of the right side: 2.28035085

Break this problem into two subproblems by setting 
(x + -5.2) equal to 2.28035085 and -2.28035085.


Subproblem 1
x + -5.2 = 2.28035085

Simplifying
x + -5.2 = 2.28035085

Reorder the terms:
-5.2 + x = 2.28035085

Solving
-5.2 + x = 2.28035085

Solving for variable 'x'.

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

Add '5.2' to each side of the equation.
-5.2 + 5.2 + x = 2.28035085 + 5.2

Combine like terms: -5.2 + 5.2 = 0.0
0.0 + x = 2.28035085 + 5.2
x = 2.28035085 + 5.2

Combine like terms: 2.28035085 + 5.2 = 7.48035085
x = 7.48035085

Simplifying
x = 7.48035085


Subproblem 2
x + -5.2 = -2.28035085

Simplifying
x + -5.2 = -2.28035085

Reorder the terms:
-5.2 + x = -2.28035085

Solving
-5.2 + x = -2.28035085

Solving for variable 'x'.

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

Add '5.2' to each side of the equation.
-5.2 + 5.2 + x = -2.28035085 + 5.2

Combine like terms: -5.2 + 5.2 = 0.0
0.0 + x = -2.28035085 + 5.2
x = -2.28035085 + 5.2

Combine like terms: -2.28035085 + 5.2 = 2.91964915
x = 2.91964915

Simplifying
x = 2.91964915


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.48035085, 2.91964915}

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