9x^2+72x+144=21

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Solution for 9x^2+72x+144=21 equation: 


Simplifying
9x2 + 72x + 144 = 21

Reorder the terms:
144 + 72x + 9x2 = 21

Solving
144 + 72x + 9x2 = 21

Solving for variable 'x'.

Reorder the terms:
144 + -21 + 72x + 9x2 = 21 + -21

Combine like terms: 144 + -21 = 123
123 + 72x + 9x2 = 21 + -21

Combine like terms: 21 + -21 = 0
123 + 72x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(41 + 24x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(41 + 24x + 3x2)' equal to zero and attempt to solve:

Simplifying
41 + 24x + 3x2 = 0

Solving
41 + 24x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
13.66666667 + 8x + x2 = 0

Move the constant term to the right:

Add '-13.66666667' to each side of the equation.
13.66666667 + 8x + -13.66666667 + x2 = 0 + -13.66666667

Reorder the terms:
13.66666667 + -13.66666667 + 8x + x2 = 0 + -13.66666667

Combine like terms: 13.66666667 + -13.66666667 = 0.00000000
0.00000000 + 8x + x2 = 0 + -13.66666667
8x + x2 = 0 + -13.66666667

Combine like terms: 0 + -13.66666667 = -13.66666667
8x + x2 = -13.66666667

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 = -13.66666667 + 16

Reorder the terms:
16 + 8x + x2 = -13.66666667 + 16

Combine like terms: -13.66666667 + 16 = 2.33333333
16 + 8x + x2 = 2.33333333

Factor a perfect square on the left side:
(x + 4)(x + 4) = 2.33333333

Calculate the square root of the right side: 1.527525231

Break this problem into two subproblems by setting 
(x + 4) equal to 1.527525231 and -1.527525231.


Subproblem 1
x + 4 = 1.527525231

Simplifying
x + 4 = 1.527525231

Reorder the terms:
4 + x = 1.527525231

Solving
4 + x = 1.527525231

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 = 1.527525231 + -4

Combine like terms: 4 + -4 = 0
0 + x = 1.527525231 + -4
x = 1.527525231 + -4

Combine like terms: 1.527525231 + -4 = -2.472474769
x = -2.472474769

Simplifying
x = -2.472474769


Subproblem 2
x + 4 = -1.527525231

Simplifying
x + 4 = -1.527525231

Reorder the terms:
4 + x = -1.527525231

Solving
4 + x = -1.527525231

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 = -1.527525231 + -4

Combine like terms: 4 + -4 = 0
0 + x = -1.527525231 + -4
x = -1.527525231 + -4

Combine like terms: -1.527525231 + -4 = -5.527525231
x = -5.527525231

Simplifying
x = -5.527525231


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.472474769, -5.527525231}
Solution
x = {-2.472474769, -5.527525231}

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