3x^2+24x-84=0

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Solution for 3x^2+24x-84=0 equation: 


Simplifying
3x2 + 24x + -84 = 0

Reorder the terms:
-84 + 24x + 3x2 = 0

Solving
-84 + 24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + 8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-28 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-28 + 8x + x2 = 0

Solving
-28 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 8x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 8x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 8x + x2 = 0 + 28
8x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
8x + x2 = 28

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 = 28 + 16

Reorder the terms:
16 + 8x + x2 = 28 + 16

Combine like terms: 28 + 16 = 44
16 + 8x + x2 = 44

Factor a perfect square on the left side:
(x + 4)(x + 4) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(x + 4) equal to 6.633249581 and -6.633249581.


Subproblem 1
x + 4 = 6.633249581

Simplifying
x + 4 = 6.633249581

Reorder the terms:
4 + x = 6.633249581

Solving
4 + x = 6.633249581

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 = 6.633249581 + -4

Combine like terms: 4 + -4 = 0
0 + x = 6.633249581 + -4
x = 6.633249581 + -4

Combine like terms: 6.633249581 + -4 = 2.633249581
x = 2.633249581

Simplifying
x = 2.633249581


Subproblem 2
x + 4 = -6.633249581

Simplifying
x + 4 = -6.633249581

Reorder the terms:
4 + x = -6.633249581

Solving
4 + x = -6.633249581

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 = -6.633249581 + -4

Combine like terms: 4 + -4 = 0
0 + x = -6.633249581 + -4
x = -6.633249581 + -4

Combine like terms: -6.633249581 + -4 = -10.633249581
x = -10.633249581

Simplifying
x = -10.633249581


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.633249581, -10.633249581}
Solution
x = {2.633249581, -10.633249581}

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