2x*2x=(x+3)(x+3+4)

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Solution for 2x*2x=(x+3)(x+3+4) equation: 


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

Reorder the terms for easier multiplication:
2 * 2x * x = (x + 3)(x + 3 + 4)

Multiply 2 * 2
4x * x = (x + 3)(x + 3 + 4)

Multiply x * x
4x2 = (x + 3)(x + 3 + 4)

Reorder the terms:
4x2 = (3 + x)(x + 3 + 4)

Reorder the terms:
4x2 = (3 + x)(3 + 4 + x)

Combine like terms: 3 + 4 = 7
4x2 = (3 + x)(7 + x)

Multiply (3 + x) * (7 + x)
4x2 = (3(7 + x) + x(7 + x))
4x2 = ((7 * 3 + x * 3) + x(7 + x))
4x2 = ((21 + 3x) + x(7 + x))
4x2 = (21 + 3x + (7 * x + x * x))
4x2 = (21 + 3x + (7x + x2))

Combine like terms: 3x + 7x = 10x
4x2 = (21 + 10x + x2)

Solving
4x2 = 21 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
-21 + -10x + 4x2 + -1x2 = 21 + 10x + x2 + -21 + -10x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
-21 + -10x + 3x2 = 21 + 10x + x2 + -21 + -10x + -1x2

Reorder the terms:
-21 + -10x + 3x2 = 21 + -21 + 10x + -10x + x2 + -1x2

Combine like terms: 21 + -21 = 0
-21 + -10x + 3x2 = 0 + 10x + -10x + x2 + -1x2
-21 + -10x + 3x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-21 + -10x + 3x2 = 0 + x2 + -1x2
-21 + -10x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + -10x + 3x2 = 0

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

Divide each side by '3'.
-7 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -3.333333333x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -3.333333333x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3.333333333x + x2 = 0 + 7
-3.333333333x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-3.333333333x + x2 = 7

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 7 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 7 + 2.777777779

Combine like terms: 7 + 2.777777779 = 9.777777779
2.777777779 + -3.333333333x + x2 = 9.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 9.777777779

Calculate the square root of the right side: 3.12694384

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 3.12694384 and -3.12694384.


Subproblem 1
x + -1.666666667 = 3.12694384

Simplifying
x + -1.666666667 = 3.12694384

Reorder the terms:
-1.666666667 + x = 3.12694384

Solving
-1.666666667 + x = 3.12694384

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 3.12694384 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 3.12694384 + 1.666666667
x = 3.12694384 + 1.666666667

Combine like terms: 3.12694384 + 1.666666667 = 4.793610507
x = 4.793610507

Simplifying
x = 4.793610507


Subproblem 2
x + -1.666666667 = -3.12694384

Simplifying
x + -1.666666667 = -3.12694384

Reorder the terms:
-1.666666667 + x = -3.12694384

Solving
-1.666666667 + x = -3.12694384

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -3.12694384 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -3.12694384 + 1.666666667
x = -3.12694384 + 1.666666667

Combine like terms: -3.12694384 + 1.666666667 = -1.460277173
x = -1.460277173

Simplifying
x = -1.460277173


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.793610507, -1.460277173}

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