4x^2+84x+72=0

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Solution for 4x^2+84x+72=0 equation: 


Simplifying
4x2 + 84x + 72 = 0

Reorder the terms:
72 + 84x + 4x2 = 0

Solving
72 + 84x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + 21x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(18 + 21x + x2)' equal to zero and attempt to solve:

Simplifying
18 + 21x + x2 = 0

Solving
18 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 21x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + 21x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 21x + x2 = 0 + -18
21x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
21x + x2 = -18

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = -18 + 110.25

Reorder the terms:
110.25 + 21x + x2 = -18 + 110.25

Combine like terms: -18 + 110.25 = 92.25
110.25 + 21x + x2 = 92.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 92.25

Calculate the square root of the right side: 9.604686356

Break this problem into two subproblems by setting 
(x + 10.5) equal to 9.604686356 and -9.604686356.


Subproblem 1
x + 10.5 = 9.604686356

Simplifying
x + 10.5 = 9.604686356

Reorder the terms:
10.5 + x = 9.604686356

Solving
10.5 + x = 9.604686356

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 9.604686356 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 9.604686356 + -10.5
x = 9.604686356 + -10.5

Combine like terms: 9.604686356 + -10.5 = -0.895313644
x = -0.895313644

Simplifying
x = -0.895313644


Subproblem 2
x + 10.5 = -9.604686356

Simplifying
x + 10.5 = -9.604686356

Reorder the terms:
10.5 + x = -9.604686356

Solving
10.5 + x = -9.604686356

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -9.604686356 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -9.604686356 + -10.5
x = -9.604686356 + -10.5

Combine like terms: -9.604686356 + -10.5 = -20.104686356
x = -20.104686356

Simplifying
x = -20.104686356


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.895313644, -20.104686356}
Solution
x = {-0.895313644, -20.104686356}

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