9x^2+2x-432=0

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Solution for 9x^2+2x-432=0 equation: 


Simplifying
9x2 + 2x + -432 = 0

Reorder the terms:
-432 + 2x + 9x2 = 0

Solving
-432 + 2x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-48 + 0.2222222222x + x2 = 0

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 0.2222222222x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 0.2222222222x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 0.2222222222x + x2 = 0 + 48
0.2222222222x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
0.2222222222x + x2 = 48

The x term is 0.2222222222x.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222x + 0.01234567901 + x2 = 48 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222x + x2 = 48 + 0.01234567901

Combine like terms: 48 + 0.01234567901 = 48.01234567901
0.01234567901 + 0.2222222222x + x2 = 48.01234567901

Factor a perfect square on the left side:
(x + 0.1111111111)(x + 0.1111111111) = 48.01234567901

Calculate the square root of the right side: 6.929094146

Break this problem into two subproblems by setting 
(x + 0.1111111111) equal to 6.929094146 and -6.929094146.


Subproblem 1
x + 0.1111111111 = 6.929094146

Simplifying
x + 0.1111111111 = 6.929094146

Reorder the terms:
0.1111111111 + x = 6.929094146

Solving
0.1111111111 + x = 6.929094146

Solving for variable 'x'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + x = 6.929094146 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + x = 6.929094146 + -0.1111111111
x = 6.929094146 + -0.1111111111

Combine like terms: 6.929094146 + -0.1111111111 = 6.8179830349
x = 6.8179830349

Simplifying
x = 6.8179830349


Subproblem 2
x + 0.1111111111 = -6.929094146

Simplifying
x + 0.1111111111 = -6.929094146

Reorder the terms:
0.1111111111 + x = -6.929094146

Solving
0.1111111111 + x = -6.929094146

Solving for variable 'x'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + x = -6.929094146 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + x = -6.929094146 + -0.1111111111
x = -6.929094146 + -0.1111111111

Combine like terms: -6.929094146 + -0.1111111111 = -7.0402052571
x = -7.0402052571

Simplifying
x = -7.0402052571


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.8179830349, -7.0402052571}

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