3x^2+72x=12534

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Solution for 3x^2+72x=12534 equation: 


Simplifying
3x2 + 72x = 12534

Reorder the terms:
72x + 3x2 = 12534

Solving
72x + 3x2 = 12534

Solving for variable 'x'.

Reorder the terms:
-12534 + 72x + 3x2 = 12534 + -12534

Combine like terms: 12534 + -12534 = 0
-12534 + 72x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4178 + 24x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4178 + 24x + x2)' equal to zero and attempt to solve:

Simplifying
-4178 + 24x + x2 = 0

Solving
-4178 + 24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4178' to each side of the equation.
-4178 + 24x + 4178 + x2 = 0 + 4178

Reorder the terms:
-4178 + 4178 + 24x + x2 = 0 + 4178

Combine like terms: -4178 + 4178 = 0
0 + 24x + x2 = 0 + 4178
24x + x2 = 0 + 4178

Combine like terms: 0 + 4178 = 4178
24x + x2 = 4178

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = 4178 + 144

Reorder the terms:
144 + 24x + x2 = 4178 + 144

Combine like terms: 4178 + 144 = 4322
144 + 24x + x2 = 4322

Factor a perfect square on the left side:
(x + 12)(x + 12) = 4322

Calculate the square root of the right side: 65.741919656

Break this problem into two subproblems by setting 
(x + 12) equal to 65.741919656 and -65.741919656.


Subproblem 1
x + 12 = 65.741919656

Simplifying
x + 12 = 65.741919656

Reorder the terms:
12 + x = 65.741919656

Solving
12 + x = 65.741919656

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = 65.741919656 + -12

Combine like terms: 12 + -12 = 0
0 + x = 65.741919656 + -12
x = 65.741919656 + -12

Combine like terms: 65.741919656 + -12 = 53.741919656
x = 53.741919656

Simplifying
x = 53.741919656


Subproblem 2
x + 12 = -65.741919656

Simplifying
x + 12 = -65.741919656

Reorder the terms:
12 + x = -65.741919656

Solving
12 + x = -65.741919656

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = -65.741919656 + -12

Combine like terms: 12 + -12 = 0
0 + x = -65.741919656 + -12
x = -65.741919656 + -12

Combine like terms: -65.741919656 + -12 = -77.741919656
x = -77.741919656

Simplifying
x = -77.741919656


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {53.741919656, -77.741919656}
Solution
x = {53.741919656, -77.741919656}

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