42x^2-478x-2460=0

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Solution for 42x^2-478x-2460=0 equation: 


Simplifying
42x2 + -478x + -2460 = 0

Reorder the terms:
-2460 + -478x + 42x2 = 0

Solving
-2460 + -478x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1230 + -239x + 21x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1230 + -239x + 21x2)' equal to zero and attempt to solve:

Simplifying
-1230 + -239x + 21x2 = 0

Solving
-1230 + -239x + 21x2 = 0

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

Divide each side by '21'.
-58.57142857 + -11.38095238x + x2 = 0

Move the constant term to the right:

Add '58.57142857' to each side of the equation.
-58.57142857 + -11.38095238x + 58.57142857 + x2 = 0 + 58.57142857

Reorder the terms:
-58.57142857 + 58.57142857 + -11.38095238x + x2 = 0 + 58.57142857

Combine like terms: -58.57142857 + 58.57142857 = 0.00000000
0.00000000 + -11.38095238x + x2 = 0 + 58.57142857
-11.38095238x + x2 = 0 + 58.57142857

Combine like terms: 0 + 58.57142857 = 58.57142857
-11.38095238x + x2 = 58.57142857

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 = 58.57142857 + 32.38151927

Reorder the terms:
32.38151927 + -11.38095238x + x2 = 58.57142857 + 32.38151927

Combine like terms: 58.57142857 + 32.38151927 = 90.95294784
32.38151927 + -11.38095238x + x2 = 90.95294784

Factor a perfect square on the left side:
(x + -5.69047619)(x + -5.69047619) = 90.95294784

Calculate the square root of the right side: 9.536925492

Break this problem into two subproblems by setting 
(x + -5.69047619) equal to 9.536925492 and -9.536925492.


Subproblem 1
x + -5.69047619 = 9.536925492

Simplifying
x + -5.69047619 = 9.536925492

Reorder the terms:
-5.69047619 + x = 9.536925492

Solving
-5.69047619 + x = 9.536925492

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 = 9.536925492 + 5.69047619

Combine like terms: -5.69047619 + 5.69047619 = 0.00000000
0.00000000 + x = 9.536925492 + 5.69047619
x = 9.536925492 + 5.69047619

Combine like terms: 9.536925492 + 5.69047619 = 15.227401682
x = 15.227401682

Simplifying
x = 15.227401682


Subproblem 2
x + -5.69047619 = -9.536925492

Simplifying
x + -5.69047619 = -9.536925492

Reorder the terms:
-5.69047619 + x = -9.536925492

Solving
-5.69047619 + x = -9.536925492

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 = -9.536925492 + 5.69047619

Combine like terms: -5.69047619 + 5.69047619 = 0.00000000
0.00000000 + x = -9.536925492 + 5.69047619
x = -9.536925492 + 5.69047619

Combine like terms: -9.536925492 + 5.69047619 = -3.846449302
x = -3.846449302

Simplifying
x = -3.846449302


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.227401682, -3.846449302}
Solution
x = {15.227401682, -3.846449302}

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