42x^2-476x-2464=0

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Solution for 42x^2-476x-2464=0 equation: 


Simplifying
42x2 + -476x + -2464 = 0

Reorder the terms:
-2464 + -476x + 42x2 = 0

Solving
-2464 + -476x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14'.
14(-176 + -34x + 3x2) = 0

Ignore the factor 14.

Subproblem 1
Set the factor '(-176 + -34x + 3x2)' equal to zero and attempt to solve:

Simplifying
-176 + -34x + 3x2 = 0

Solving
-176 + -34x + 3x2 = 0

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

Divide each side by '3'.
-58.66666667 + -11.33333333x + x2 = 0

Move the constant term to the right:

Add '58.66666667' to each side of the equation.
-58.66666667 + -11.33333333x + 58.66666667 + x2 = 0 + 58.66666667

Reorder the terms:
-58.66666667 + 58.66666667 + -11.33333333x + x2 = 0 + 58.66666667

Combine like terms: -58.66666667 + 58.66666667 = 0.00000000
0.00000000 + -11.33333333x + x2 = 0 + 58.66666667
-11.33333333x + x2 = 0 + 58.66666667

Combine like terms: 0 + 58.66666667 = 58.66666667
-11.33333333x + x2 = 58.66666667

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 = 58.66666667 + 32.11111109

Reorder the terms:
32.11111109 + -11.33333333x + x2 = 58.66666667 + 32.11111109

Combine like terms: 58.66666667 + 32.11111109 = 90.77777776
32.11111109 + -11.33333333x + x2 = 90.77777776

Factor a perfect square on the left side:
(x + -5.666666665)(x + -5.666666665) = 90.77777776

Calculate the square root of the right side: 9.527737284

Break this problem into two subproblems by setting 
(x + -5.666666665) equal to 9.527737284 and -9.527737284.


Subproblem 1
x + -5.666666665 = 9.527737284

Simplifying
x + -5.666666665 = 9.527737284

Reorder the terms:
-5.666666665 + x = 9.527737284

Solving
-5.666666665 + x = 9.527737284

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 = 9.527737284 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = 9.527737284 + 5.666666665
x = 9.527737284 + 5.666666665

Combine like terms: 9.527737284 + 5.666666665 = 15.194403949
x = 15.194403949

Simplifying
x = 15.194403949


Subproblem 2
x + -5.666666665 = -9.527737284

Simplifying
x + -5.666666665 = -9.527737284

Reorder the terms:
-5.666666665 + x = -9.527737284

Solving
-5.666666665 + x = -9.527737284

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 = -9.527737284 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = -9.527737284 + 5.666666665
x = -9.527737284 + 5.666666665

Combine like terms: -9.527737284 + 5.666666665 = -3.861070619
x = -3.861070619

Simplifying
x = -3.861070619


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.194403949, -3.861070619}
Solution
x = {15.194403949, -3.861070619}

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