3X^2-14X-7=0

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Solution for 3X^2-14X-7=0 equation: 


Simplifying
3X2 + -14X + -7 = 0

Reorder the terms:
-7 + -14X + 3X2 = 0

Solving
-7 + -14X + 3X2 = 0

Solving for variable 'X'.

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

Divide each side by '3'.
-2.333333333 + -4.666666667X + X2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -4.666666667X + 2.333333333 + X2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -4.666666667X + X2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -4.666666667X + X2 = 0 + 2.333333333
-4.666666667X + X2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-4.666666667X + X2 = 2.333333333

The X term is -4.666666667X.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667X + 5.444444448 + X2 = 2.333333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667X + X2 = 2.333333333 + 5.444444448

Combine like terms: 2.333333333 + 5.444444448 = 7.777777781
5.444444448 + -4.666666667X + X2 = 7.777777781

Factor a perfect square on the left side:
(X + -2.333333334)(X + -2.333333334) = 7.777777781

Calculate the square root of the right side: 2.788866756

Break this problem into two subproblems by setting 
(X + -2.333333334) equal to 2.788866756 and -2.788866756.


Subproblem 1
X + -2.333333334 = 2.788866756

Simplifying
X + -2.333333334 = 2.788866756

Reorder the terms:
-2.333333334 + X = 2.788866756

Solving
-2.333333334 + X = 2.788866756

Solving for variable 'X'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + X = 2.788866756 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + X = 2.788866756 + 2.333333334
X = 2.788866756 + 2.333333334

Combine like terms: 2.788866756 + 2.333333334 = 5.12220009
X = 5.12220009

Simplifying
X = 5.12220009


Subproblem 2
X + -2.333333334 = -2.788866756

Simplifying
X + -2.333333334 = -2.788866756

Reorder the terms:
-2.333333334 + X = -2.788866756

Solving
-2.333333334 + X = -2.788866756

Solving for variable 'X'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + X = -2.788866756 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + X = -2.788866756 + 2.333333334
X = -2.788866756 + 2.333333334

Combine like terms: -2.788866756 + 2.333333334 = -0.455533422
X = -0.455533422

Simplifying
X = -0.455533422


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {5.12220009, -0.455533422}

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