9x^2+288x+1530=0

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Solution for 9x^2+288x+1530=0 equation: 


Simplifying
9x2 + 288x + 1530 = 0

Reorder the terms:
1530 + 288x + 9x2 = 0

Solving
1530 + 288x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(170 + 32x + x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(170 + 32x + x2)' equal to zero and attempt to solve:

Simplifying
170 + 32x + x2 = 0

Solving
170 + 32x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-170' to each side of the equation.
170 + 32x + -170 + x2 = 0 + -170

Reorder the terms:
170 + -170 + 32x + x2 = 0 + -170

Combine like terms: 170 + -170 = 0
0 + 32x + x2 = 0 + -170
32x + x2 = 0 + -170

Combine like terms: 0 + -170 = -170
32x + x2 = -170

The x term is 32x.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32x + 256 + x2 = -170 + 256

Reorder the terms:
256 + 32x + x2 = -170 + 256

Combine like terms: -170 + 256 = 86
256 + 32x + x2 = 86

Factor a perfect square on the left side:
(x + 16)(x + 16) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(x + 16) equal to 9.273618495 and -9.273618495.


Subproblem 1
x + 16 = 9.273618495

Simplifying
x + 16 = 9.273618495

Reorder the terms:
16 + x = 9.273618495

Solving
16 + x = 9.273618495

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = 9.273618495 + -16

Combine like terms: 16 + -16 = 0
0 + x = 9.273618495 + -16
x = 9.273618495 + -16

Combine like terms: 9.273618495 + -16 = -6.726381505
x = -6.726381505

Simplifying
x = -6.726381505


Subproblem 2
x + 16 = -9.273618495

Simplifying
x + 16 = -9.273618495

Reorder the terms:
16 + x = -9.273618495

Solving
16 + x = -9.273618495

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = -9.273618495 + -16

Combine like terms: 16 + -16 = 0
0 + x = -9.273618495 + -16
x = -9.273618495 + -16

Combine like terms: -9.273618495 + -16 = -25.273618495
x = -25.273618495

Simplifying
x = -25.273618495


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-6.726381505, -25.273618495}
Solution
x = {-6.726381505, -25.273618495}

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