6X^2-5X-10=0

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Solution for 6X^2-5X-10=0 equation: 


Simplifying
6X2 + -5X + -10 = 0

Reorder the terms:
-10 + -5X + 6X2 = 0

Solving
-10 + -5X + 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'.
-1.666666667 + -0.8333333333X + X2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -0.8333333333X + 1.666666667 + X2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -0.8333333333X + X2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -0.8333333333X + X2 = 0 + 1.666666667
-0.8333333333X + X2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-0.8333333333X + X2 = 1.666666667

The X term is -0.8333333333X.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333X + 0.1736111111 + X2 = 1.666666667 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333X + X2 = 1.666666667 + 0.1736111111

Combine like terms: 1.666666667 + 0.1736111111 = 1.8402777781
0.1736111111 + -0.8333333333X + X2 = 1.8402777781

Factor a perfect square on the left side:
(X + -0.4166666667)(X + -0.4166666667) = 1.8402777781

Calculate the square root of the right side: 1.356568383

Break this problem into two subproblems by setting 
(X + -0.4166666667) equal to 1.356568383 and -1.356568383.


Subproblem 1
X + -0.4166666667 = 1.356568383

Simplifying
X + -0.4166666667 = 1.356568383

Reorder the terms:
-0.4166666667 + X = 1.356568383

Solving
-0.4166666667 + X = 1.356568383

Solving for variable 'X'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + X = 1.356568383 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + X = 1.356568383 + 0.4166666667
X = 1.356568383 + 0.4166666667

Combine like terms: 1.356568383 + 0.4166666667 = 1.7732350497
X = 1.7732350497

Simplifying
X = 1.7732350497


Subproblem 2
X + -0.4166666667 = -1.356568383

Simplifying
X + -0.4166666667 = -1.356568383

Reorder the terms:
-0.4166666667 + X = -1.356568383

Solving
-0.4166666667 + X = -1.356568383

Solving for variable 'X'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + X = -1.356568383 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + X = -1.356568383 + 0.4166666667
X = -1.356568383 + 0.4166666667

Combine like terms: -1.356568383 + 0.4166666667 = -0.9399017163
X = -0.9399017163

Simplifying
X = -0.9399017163


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.7732350497, -0.9399017163}

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