3x^2-9x-57=0

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Solution for 3x^2-9x-57=0 equation: 


Simplifying
3x2 + -9x + -57 = 0

Reorder the terms:
-57 + -9x + 3x2 = 0

Solving
-57 + -9x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-19 + -3x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-19 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-19 + -3x + x2 = 0

Solving
-19 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -3x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + -3x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -3x + x2 = 0 + 19
-3x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
-3x + x2 = 19

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 19 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 19 + 2.25

Combine like terms: 19 + 2.25 = 21.25
2.25 + -3x + x2 = 21.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
x + -1.5 = 4.609772229

Simplifying
x + -1.5 = 4.609772229

Reorder the terms:
-1.5 + x = 4.609772229

Solving
-1.5 + x = 4.609772229

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 4.609772229 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4.609772229 + 1.5
x = 4.609772229 + 1.5

Combine like terms: 4.609772229 + 1.5 = 6.109772229
x = 6.109772229

Simplifying
x = 6.109772229


Subproblem 2
x + -1.5 = -4.609772229

Simplifying
x + -1.5 = -4.609772229

Reorder the terms:
-1.5 + x = -4.609772229

Solving
-1.5 + x = -4.609772229

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -4.609772229 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4.609772229 + 1.5
x = -4.609772229 + 1.5

Combine like terms: -4.609772229 + 1.5 = -3.109772229
x = -3.109772229

Simplifying
x = -3.109772229


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.109772229, -3.109772229}
Solution
x = {6.109772229, -3.109772229}

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