0=42x^2-478x-2462

Solution for 0=42x^2-478x-2462 equation:

Simplifying
0 = 42x2 + -478x + -2462

Reorder the terms:
0 = -2462 + -478x + 42x2

Solving
0 = -2462 + -478x + 42x2

Solving for variable 'x'.

Combine like terms: 0 + 2462 = 2462
2462 + 478x + -42x2 = -2462 + -478x + 42x2 + 2462 + 478x + -42x2

Reorder the terms:
2462 + 478x + -42x2 = -2462 + 2462 + -478x + 478x + 42x2 + -42x2

Combine like terms: -2462 + 2462 = 0
2462 + 478x + -42x2 = 0 + -478x + 478x + 42x2 + -42x2
2462 + 478x + -42x2 = -478x + 478x + 42x2 + -42x2

Combine like terms: -478x + 478x = 0
2462 + 478x + -42x2 = 0 + 42x2 + -42x2
2462 + 478x + -42x2 = 42x2 + -42x2

Combine like terms: 42x2 + -42x2 = 0
2462 + 478x + -42x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1231 + 239x + -21x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1231 + 239x + -21x2)' equal to zero and attempt to solve:

Simplifying
1231 + 239x + -21x2 = 0

Solving
1231 + 239x + -21x2 = 0

Begin completing the square.  Divide all terms by
-21 the coefficient of the squared term: 

Divide each side by '-21'.
-58.61904762 + -11.38095238x + x2 = 0

Move the constant term to the right:

Add '58.61904762' to each side of the equation.
-58.61904762 + -11.38095238x + 58.61904762 + x2 = 0 + 58.61904762

Reorder the terms:
-58.61904762 + 58.61904762 + -11.38095238x + x2 = 0 + 58.61904762

Combine like terms: -58.61904762 + 58.61904762 = 0.00000000
0.00000000 + -11.38095238x + x2 = 0 + 58.61904762
-11.38095238x + x2 = 0 + 58.61904762

Combine like terms: 0 + 58.61904762 = 58.61904762
-11.38095238x + x2 = 58.61904762

The x term is -11.38095238x.  Take half its coefficient (-5.69047619).
Square it (32.38151927) and add it to both sides.

Add '32.38151927' to each side of the equation.
-11.38095238x + 32.38151927 + x2 = 58.61904762 + 32.38151927

Reorder the terms:
32.38151927 + -11.38095238x + x2 = 58.61904762 + 32.38151927

Combine like terms: 58.61904762 + 32.38151927 = 91.00056689
32.38151927 + -11.38095238x + x2 = 91.00056689

Factor a perfect square on the left side:
(x + -5.69047619)(x + -5.69047619) = 91.00056689

Calculate the square root of the right side: 9.539421727

Break this problem into two subproblems by setting 
(x + -5.69047619) equal to 9.539421727 and -9.539421727.

Subproblem 1
x + -5.69047619 = 9.539421727

Simplifying
x + -5.69047619 = 9.539421727

Reorder the terms:
-5.69047619 + x = 9.539421727

Solving
-5.69047619 + x = 9.539421727

Solving for variable 'x'.

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

Add '5.69047619' to each side of the equation.
-5.69047619 + 5.69047619 + x = 9.539421727 + 5.69047619

Combine like terms: -5.69047619 + 5.69047619 = 0.00000000
0.00000000 + x = 9.539421727 + 5.69047619
x = 9.539421727 + 5.69047619

Combine like terms: 9.539421727 + 5.69047619 = 15.229897917
x = 15.229897917

Simplifying
x = 15.229897917

Subproblem 2
x + -5.69047619 = -9.539421727

Simplifying
x + -5.69047619 = -9.539421727

Reorder the terms:
-5.69047619 + x = -9.539421727

Solving
-5.69047619 + x = -9.539421727

Solving for variable 'x'.

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

Add '5.69047619' to each side of the equation.
-5.69047619 + 5.69047619 + x = -9.539421727 + 5.69047619

Combine like terms: -5.69047619 + 5.69047619 = 0.00000000
0.00000000 + x = -9.539421727 + 5.69047619
x = -9.539421727 + 5.69047619

Combine like terms: -9.539421727 + 5.69047619 = -3.848945537
x = -3.848945537

Simplifying
x = -3.848945537

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.229897917, -3.848945537}
Solution
x = {15.229897917, -3.848945537}