42X^2-7X-4=0

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Solution for 42X^2-7X-4=0 equation: 


Simplifying
42X2 + -7X + -4 = 0

Reorder the terms:
-4 + -7X + 42X2 = 0

Solving
-4 + -7X + 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'.
-0.09523809524 + -0.1666666667X + X2 = 0

Move the constant term to the right:

Add '0.09523809524' to each side of the equation.
-0.09523809524 + -0.1666666667X + 0.09523809524 + X2 = 0 + 0.09523809524

Reorder the terms:
-0.09523809524 + 0.09523809524 + -0.1666666667X + X2 = 0 + 0.09523809524

Combine like terms: -0.09523809524 + 0.09523809524 = 0.00000000000
0.00000000000 + -0.1666666667X + X2 = 0 + 0.09523809524
-0.1666666667X + X2 = 0 + 0.09523809524

Combine like terms: 0 + 0.09523809524 = 0.09523809524
-0.1666666667X + X2 = 0.09523809524

The X term is -0.1666666667X.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667X + 0.006944444447 + X2 = 0.09523809524 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667X + X2 = 0.09523809524 + 0.006944444447

Combine like terms: 0.09523809524 + 0.006944444447 = 0.102182539687
0.006944444447 + -0.1666666667X + X2 = 0.102182539687

Factor a perfect square on the left side:
(X + -0.08333333335)(X + -0.08333333335) = 0.102182539687

Calculate the square root of the right side: 0.319660038

Break this problem into two subproblems by setting 
(X + -0.08333333335) equal to 0.319660038 and -0.319660038.


Subproblem 1
X + -0.08333333335 = 0.319660038

Simplifying
X + -0.08333333335 = 0.319660038

Reorder the terms:
-0.08333333335 + X = 0.319660038

Solving
-0.08333333335 + X = 0.319660038

Solving for variable 'X'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + X = 0.319660038 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + X = 0.319660038 + 0.08333333335
X = 0.319660038 + 0.08333333335

Combine like terms: 0.319660038 + 0.08333333335 = 0.40299337135
X = 0.40299337135

Simplifying
X = 0.40299337135


Subproblem 2
X + -0.08333333335 = -0.319660038

Simplifying
X + -0.08333333335 = -0.319660038

Reorder the terms:
-0.08333333335 + X = -0.319660038

Solving
-0.08333333335 + X = -0.319660038

Solving for variable 'X'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + X = -0.319660038 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + X = -0.319660038 + 0.08333333335
X = -0.319660038 + 0.08333333335

Combine like terms: -0.319660038 + 0.08333333335 = -0.23632670465
X = -0.23632670465

Simplifying
X = -0.23632670465


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.40299337135, -0.23632670465}

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