42x^2-476x-2465=0

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Solution for 42x^2-476x-2465=0 equation: 


Simplifying
42x2 + -476x + -2465 = 0

Reorder the terms:
-2465 + -476x + 42x2 = 0

Solving
-2465 + -476x + 42x2 = 0

Solving for variable 'x'.

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

Divide each side by '42'.
-58.69047619 + -11.33333333x + x2 = 0

Move the constant term to the right:

Add '58.69047619' to each side of the equation.
-58.69047619 + -11.33333333x + 58.69047619 + x2 = 0 + 58.69047619

Reorder the terms:
-58.69047619 + 58.69047619 + -11.33333333x + x2 = 0 + 58.69047619

Combine like terms: -58.69047619 + 58.69047619 = 0.00000000
0.00000000 + -11.33333333x + x2 = 0 + 58.69047619
-11.33333333x + x2 = 0 + 58.69047619

Combine like terms: 0 + 58.69047619 = 58.69047619
-11.33333333x + x2 = 58.69047619

The x term is -11.33333333x.  Take half its coefficient (-5.666666665).
Square it (32.11111109) and add it to both sides.

Add '32.11111109' to each side of the equation.
-11.33333333x + 32.11111109 + x2 = 58.69047619 + 32.11111109

Reorder the terms:
32.11111109 + -11.33333333x + x2 = 58.69047619 + 32.11111109

Combine like terms: 58.69047619 + 32.11111109 = 90.80158728
32.11111109 + -11.33333333x + x2 = 90.80158728

Factor a perfect square on the left side:
(x + -5.666666665)(x + -5.666666665) = 90.80158728

Calculate the square root of the right side: 9.528986687

Break this problem into two subproblems by setting 
(x + -5.666666665) equal to 9.528986687 and -9.528986687.


Subproblem 1
x + -5.666666665 = 9.528986687

Simplifying
x + -5.666666665 = 9.528986687

Reorder the terms:
-5.666666665 + x = 9.528986687

Solving
-5.666666665 + x = 9.528986687

Solving for variable 'x'.

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

Add '5.666666665' to each side of the equation.
-5.666666665 + 5.666666665 + x = 9.528986687 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = 9.528986687 + 5.666666665
x = 9.528986687 + 5.666666665

Combine like terms: 9.528986687 + 5.666666665 = 15.195653352
x = 15.195653352

Simplifying
x = 15.195653352


Subproblem 2
x + -5.666666665 = -9.528986687

Simplifying
x + -5.666666665 = -9.528986687

Reorder the terms:
-5.666666665 + x = -9.528986687

Solving
-5.666666665 + x = -9.528986687

Solving for variable 'x'.

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

Add '5.666666665' to each side of the equation.
-5.666666665 + 5.666666665 + x = -9.528986687 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = -9.528986687 + 5.666666665
x = -9.528986687 + 5.666666665

Combine like terms: -9.528986687 + 5.666666665 = -3.862320022
x = -3.862320022

Simplifying
x = -3.862320022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.195653352, -3.862320022}

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