3x^2+24x+12=528

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Solution for 3x^2+24x+12=528 equation: 


Simplifying
3x2 + 24x + 12 = 528

Reorder the terms:
12 + 24x + 3x2 = 528

Solving
12 + 24x + 3x2 = 528

Solving for variable 'x'.

Reorder the terms:
12 + -528 + 24x + 3x2 = 528 + -528

Combine like terms: 12 + -528 = -516
-516 + 24x + 3x2 = 528 + -528

Combine like terms: 528 + -528 = 0
-516 + 24x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-172 + 8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-172 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-172 + 8x + x2 = 0

Solving
-172 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '172' to each side of the equation.
-172 + 8x + 172 + x2 = 0 + 172

Reorder the terms:
-172 + 172 + 8x + x2 = 0 + 172

Combine like terms: -172 + 172 = 0
0 + 8x + x2 = 0 + 172
8x + x2 = 0 + 172

Combine like terms: 0 + 172 = 172
8x + x2 = 172

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 172 + 16

Reorder the terms:
16 + 8x + x2 = 172 + 16

Combine like terms: 172 + 16 = 188
16 + 8x + x2 = 188

Factor a perfect square on the left side:
(x + 4)(x + 4) = 188

Calculate the square root of the right side: 13.711309201

Break this problem into two subproblems by setting 
(x + 4) equal to 13.711309201 and -13.711309201.


Subproblem 1
x + 4 = 13.711309201

Simplifying
x + 4 = 13.711309201

Reorder the terms:
4 + x = 13.711309201

Solving
4 + x = 13.711309201

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 13.711309201 + -4

Combine like terms: 4 + -4 = 0
0 + x = 13.711309201 + -4
x = 13.711309201 + -4

Combine like terms: 13.711309201 + -4 = 9.711309201
x = 9.711309201

Simplifying
x = 9.711309201


Subproblem 2
x + 4 = -13.711309201

Simplifying
x + 4 = -13.711309201

Reorder the terms:
4 + x = -13.711309201

Solving
4 + x = -13.711309201

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -13.711309201 + -4

Combine like terms: 4 + -4 = 0
0 + x = -13.711309201 + -4
x = -13.711309201 + -4

Combine like terms: -13.711309201 + -4 = -17.711309201
x = -17.711309201

Simplifying
x = -17.711309201


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.711309201, -17.711309201}
Solution
x = {9.711309201, -17.711309201}

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