6X^2-28X-15=0

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Solution for 6X^2-28X-15=0 equation: 


Simplifying
6X2 + -28X + -15 = 0

Reorder the terms:
-15 + -28X + 6X2 = 0

Solving
-15 + -28X + 6X2 = 0

Solving for variable 'X'.

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

Divide each side by '6'.
-2.5 + -4.666666667X + X2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -4.666666667X + 2.5 + X2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -4.666666667X + X2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -4.666666667X + X2 = 0 + 2.5
-4.666666667X + X2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-4.666666667X + X2 = 2.5

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 = 2.5 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667X + X2 = 2.5 + 5.444444448

Combine like terms: 2.5 + 5.444444448 = 7.944444448
5.444444448 + -4.666666667X + X2 = 7.944444448

Factor a perfect square on the left side:
(X + -2.333333334)(X + -2.333333334) = 7.944444448

Calculate the square root of the right side: 2.818589088

Break this problem into two subproblems by setting 
(X + -2.333333334) equal to 2.818589088 and -2.818589088.


Subproblem 1
X + -2.333333334 = 2.818589088

Simplifying
X + -2.333333334 = 2.818589088

Reorder the terms:
-2.333333334 + X = 2.818589088

Solving
-2.333333334 + X = 2.818589088

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 = 2.818589088 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + X = 2.818589088 + 2.333333334
X = 2.818589088 + 2.333333334

Combine like terms: 2.818589088 + 2.333333334 = 5.151922422
X = 5.151922422

Simplifying
X = 5.151922422


Subproblem 2
X + -2.333333334 = -2.818589088

Simplifying
X + -2.333333334 = -2.818589088

Reorder the terms:
-2.333333334 + X = -2.818589088

Solving
-2.333333334 + X = -2.818589088

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 = -2.818589088 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + X = -2.818589088 + 2.333333334
X = -2.818589088 + 2.333333334

Combine like terms: -2.818589088 + 2.333333334 = -0.485255754
X = -0.485255754

Simplifying
X = -0.485255754


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {5.151922422, -0.485255754}

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