9x^2-423x-1566=0

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Solution for 9x^2-423x-1566=0 equation: 


Simplifying
9x2 + -423x + -1566 = 0

Reorder the terms:
-1566 + -423x + 9x2 = 0

Solving
-1566 + -423x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-174 + -47x + x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-174 + -47x + x2)' equal to zero and attempt to solve:

Simplifying
-174 + -47x + x2 = 0

Solving
-174 + -47x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '174' to each side of the equation.
-174 + -47x + 174 + x2 = 0 + 174

Reorder the terms:
-174 + 174 + -47x + x2 = 0 + 174

Combine like terms: -174 + 174 = 0
0 + -47x + x2 = 0 + 174
-47x + x2 = 0 + 174

Combine like terms: 0 + 174 = 174
-47x + x2 = 174

The x term is -47x.  Take half its coefficient (-23.5).
Square it (552.25) and add it to both sides.

Add '552.25' to each side of the equation.
-47x + 552.25 + x2 = 174 + 552.25

Reorder the terms:
552.25 + -47x + x2 = 174 + 552.25

Combine like terms: 174 + 552.25 = 726.25
552.25 + -47x + x2 = 726.25

Factor a perfect square on the left side:
(x + -23.5)(x + -23.5) = 726.25

Calculate the square root of the right side: 26.949025956

Break this problem into two subproblems by setting 
(x + -23.5) equal to 26.949025956 and -26.949025956.


Subproblem 1
x + -23.5 = 26.949025956

Simplifying
x + -23.5 = 26.949025956

Reorder the terms:
-23.5 + x = 26.949025956

Solving
-23.5 + x = 26.949025956

Solving for variable 'x'.

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

Add '23.5' to each side of the equation.
-23.5 + 23.5 + x = 26.949025956 + 23.5

Combine like terms: -23.5 + 23.5 = 0.0
0.0 + x = 26.949025956 + 23.5
x = 26.949025956 + 23.5

Combine like terms: 26.949025956 + 23.5 = 50.449025956
x = 50.449025956

Simplifying
x = 50.449025956


Subproblem 2
x + -23.5 = -26.949025956

Simplifying
x + -23.5 = -26.949025956

Reorder the terms:
-23.5 + x = -26.949025956

Solving
-23.5 + x = -26.949025956

Solving for variable 'x'.

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

Add '23.5' to each side of the equation.
-23.5 + 23.5 + x = -26.949025956 + 23.5

Combine like terms: -23.5 + 23.5 = 0.0
0.0 + x = -26.949025956 + 23.5
x = -26.949025956 + 23.5

Combine like terms: -26.949025956 + 23.5 = -3.449025956
x = -3.449025956

Simplifying
x = -3.449025956


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.449025956, -3.449025956}
Solution
x = {50.449025956, -3.449025956}

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