(3x+21)(3x+21)=54

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Solution for (3x+21)(3x+21)=54 equation: 


Simplifying
(3x + 21)(3x + 21) = 54

Reorder the terms:
(21 + 3x)(3x + 21) = 54

Reorder the terms:
(21 + 3x)(21 + 3x) = 54

Multiply (21 + 3x) * (21 + 3x)
(21(21 + 3x) + 3x * (21 + 3x)) = 54
((21 * 21 + 3x * 21) + 3x * (21 + 3x)) = 54
((441 + 63x) + 3x * (21 + 3x)) = 54
(441 + 63x + (21 * 3x + 3x * 3x)) = 54
(441 + 63x + (63x + 9x2)) = 54

Combine like terms: 63x + 63x = 126x
(441 + 126x + 9x2) = 54

Solving
441 + 126x + 9x2 = 54

Solving for variable 'x'.

Reorder the terms:
441 + -54 + 126x + 9x2 = 54 + -54

Combine like terms: 441 + -54 = 387
387 + 126x + 9x2 = 54 + -54

Combine like terms: 54 + -54 = 0
387 + 126x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(43 + 14x + x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(43 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
43 + 14x + x2 = 0

Solving
43 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-43' to each side of the equation.
43 + 14x + -43 + x2 = 0 + -43

Reorder the terms:
43 + -43 + 14x + x2 = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 14x + x2 = 0 + -43
14x + x2 = 0 + -43

Combine like terms: 0 + -43 = -43
14x + x2 = -43

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -43 + 49

Reorder the terms:
49 + 14x + x2 = -43 + 49

Combine like terms: -43 + 49 = 6
49 + 14x + x2 = 6

Factor a perfect square on the left side:
(x + 7)(x + 7) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + 7) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + 7 = 2.449489743

Simplifying
x + 7 = 2.449489743

Reorder the terms:
7 + x = 2.449489743

Solving
7 + x = 2.449489743

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 2.449489743 + -7

Combine like terms: 7 + -7 = 0
0 + x = 2.449489743 + -7
x = 2.449489743 + -7

Combine like terms: 2.449489743 + -7 = -4.550510257
x = -4.550510257

Simplifying
x = -4.550510257


Subproblem 2
x + 7 = -2.449489743

Simplifying
x + 7 = -2.449489743

Reorder the terms:
7 + x = -2.449489743

Solving
7 + x = -2.449489743

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -2.449489743 + -7

Combine like terms: 7 + -7 = 0
0 + x = -2.449489743 + -7
x = -2.449489743 + -7

Combine like terms: -2.449489743 + -7 = -9.449489743
x = -9.449489743

Simplifying
x = -9.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.550510257, -9.449489743}
Solution
x = {-4.550510257, -9.449489743}

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