(10-2x)(10-2x)=48

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Solution for (10-2x)(10-2x)=48 equation: 


Simplifying
(10 + -2x)(10 + -2x) = 48

Multiply (10 + -2x) * (10 + -2x)
(10(10 + -2x) + -2x * (10 + -2x)) = 48
((10 * 10 + -2x * 10) + -2x * (10 + -2x)) = 48
((100 + -20x) + -2x * (10 + -2x)) = 48
(100 + -20x + (10 * -2x + -2x * -2x)) = 48
(100 + -20x + (-20x + 4x2)) = 48

Combine like terms: -20x + -20x = -40x
(100 + -40x + 4x2) = 48

Solving
100 + -40x + 4x2 = 48

Solving for variable 'x'.

Reorder the terms:
100 + -48 + -40x + 4x2 = 48 + -48

Combine like terms: 100 + -48 = 52
52 + -40x + 4x2 = 48 + -48

Combine like terms: 48 + -48 = 0
52 + -40x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(13 + -10x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(13 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
13 + -10x + x2 = 0

Solving
13 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -10x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + -10x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -10x + x2 = 0 + -13
-10x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-10x + x2 = -13

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -13 + 25

Reorder the terms:
25 + -10x + x2 = -13 + 25

Combine like terms: -13 + 25 = 12
25 + -10x + x2 = 12

Factor a perfect square on the left side:
(x + -5)(x + -5) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -5) equal to 3.464101615 and -3.464101615.


Subproblem 1
x + -5 = 3.464101615

Simplifying
x + -5 = 3.464101615

Reorder the terms:
-5 + x = 3.464101615

Solving
-5 + x = 3.464101615

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 3.464101615 + 5

Combine like terms: -5 + 5 = 0
0 + x = 3.464101615 + 5
x = 3.464101615 + 5

Combine like terms: 3.464101615 + 5 = 8.464101615
x = 8.464101615

Simplifying
x = 8.464101615


Subproblem 2
x + -5 = -3.464101615

Simplifying
x + -5 = -3.464101615

Reorder the terms:
-5 + x = -3.464101615

Solving
-5 + x = -3.464101615

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -3.464101615 + 5

Combine like terms: -5 + 5 = 0
0 + x = -3.464101615 + 5
x = -3.464101615 + 5

Combine like terms: -3.464101615 + 5 = 1.535898385
x = 1.535898385

Simplifying
x = 1.535898385


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.464101615, 1.535898385}
Solution
x = {8.464101615, 1.535898385}

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