(2x)2=(x+2)*(3x+7)

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Solution for (2x)2=(x+2)*(3x+7) equation: 


Simplifying
(2x) * 2 = (x + 2)(3x + 7)

Remove parenthesis around (2x)
2x * 2 = (x + 2)(3x + 7)

Reorder the terms for easier multiplication:
2 * 2x = (x + 2)(3x + 7)

Multiply 2 * 2
4x = (x + 2)(3x + 7)

Reorder the terms:
4x = (2 + x)(3x + 7)

Reorder the terms:
4x = (2 + x)(7 + 3x)

Multiply (2 + x) * (7 + 3x)
4x = (2(7 + 3x) + x(7 + 3x))
4x = ((7 * 2 + 3x * 2) + x(7 + 3x))
4x = ((14 + 6x) + x(7 + 3x))
4x = (14 + 6x + (7 * x + 3x * x))
4x = (14 + 6x + (7x + 3x2))

Combine like terms: 6x + 7x = 13x
4x = (14 + 13x + 3x2)

Solving
4x = 14 + 13x + 3x2

Solving for variable 'x'.

Reorder the terms:
-14 + 4x + -13x + -3x2 = 14 + 13x + 3x2 + -14 + -13x + -3x2

Combine like terms: 4x + -13x = -9x
-14 + -9x + -3x2 = 14 + 13x + 3x2 + -14 + -13x + -3x2

Reorder the terms:
-14 + -9x + -3x2 = 14 + -14 + 13x + -13x + 3x2 + -3x2

Combine like terms: 14 + -14 = 0
-14 + -9x + -3x2 = 0 + 13x + -13x + 3x2 + -3x2
-14 + -9x + -3x2 = 13x + -13x + 3x2 + -3x2

Combine like terms: 13x + -13x = 0
-14 + -9x + -3x2 = 0 + 3x2 + -3x2
-14 + -9x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-14 + -9x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 9x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(14 + 9x + 3x2)' equal to zero and attempt to solve:

Simplifying
14 + 9x + 3x2 = 0

Solving
14 + 9x + 3x2 = 0

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

Divide each side by '3'.
4.666666667 + 3x + x2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + 3x + -4.666666667 + x2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + 3x + x2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + 3x + x2 = 0 + -4.666666667
3x + x2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
3x + x2 = -4.666666667

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -4.666666667 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -4.666666667 + 2.25

Combine like terms: -4.666666667 + 2.25 = -2.416666667
2.25 + 3x + x2 = -2.416666667

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -2.416666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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