2(x-3)(x-3)=4

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Solution for 2(x-3)(x-3)=4 equation: 


Simplifying
2(x + -3)(x + -3) = 4

Reorder the terms:
2(-3 + x)(x + -3) = 4

Reorder the terms:
2(-3 + x)(-3 + x) = 4

Multiply (-3 + x) * (-3 + x)
2(-3(-3 + x) + x(-3 + x)) = 4
2((-3 * -3 + x * -3) + x(-3 + x)) = 4
2((9 + -3x) + x(-3 + x)) = 4
2(9 + -3x + (-3 * x + x * x)) = 4
2(9 + -3x + (-3x + x2)) = 4

Combine like terms: -3x + -3x = -6x
2(9 + -6x + x2) = 4
(9 * 2 + -6x * 2 + x2 * 2) = 4
(18 + -12x + 2x2) = 4

Solving
18 + -12x + 2x2 = 4

Solving for variable 'x'.

Reorder the terms:
18 + -4 + -12x + 2x2 = 4 + -4

Combine like terms: 18 + -4 = 14
14 + -12x + 2x2 = 4 + -4

Combine like terms: 4 + -4 = 0
14 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
7 + -6x + x2 = 0

Solving
7 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -6x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -6x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x + x2 = 0 + -7
-6x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-6x + x2 = -7

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -7 + 9

Reorder the terms:
9 + -6x + x2 = -7 + 9

Combine like terms: -7 + 9 = 2
9 + -6x + x2 = 2

Factor a perfect square on the left side:
(x + -3)(x + -3) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -3) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + -3 = 1.414213562

Simplifying
x + -3 = 1.414213562

Reorder the terms:
-3 + x = 1.414213562

Solving
-3 + x = 1.414213562

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + x = 1.414213562 + 3
x = 1.414213562 + 3

Combine like terms: 1.414213562 + 3 = 4.414213562
x = 4.414213562

Simplifying
x = 4.414213562


Subproblem 2
x + -3 = -1.414213562

Simplifying
x + -3 = -1.414213562

Reorder the terms:
-3 + x = -1.414213562

Solving
-3 + x = -1.414213562

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + x = -1.414213562 + 3
x = -1.414213562 + 3

Combine like terms: -1.414213562 + 3 = 1.585786438
x = 1.585786438

Simplifying
x = 1.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.414213562, 1.585786438}
Solution
x = {4.414213562, 1.585786438}

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