2X^2-6X-98=0

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Solution for 2X^2-6X-98=0 equation: 


Simplifying
2X2 + -6X + -98 = 0

Reorder the terms:
-98 + -6X + 2X2 = 0

Solving
-98 + -6X + 2X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-49 + -3X + X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-49 + -3X + X2)' equal to zero and attempt to solve:

Simplifying
-49 + -3X + X2 = 0

Solving
-49 + -3X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -3X + 49 + X2 = 0 + 49

Reorder the terms:
-49 + 49 + -3X + X2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -3X + X2 = 0 + 49
-3X + X2 = 0 + 49

Combine like terms: 0 + 49 = 49
-3X + X2 = 49

The X term is -3X.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3X + 2.25 + X2 = 49 + 2.25

Reorder the terms:
2.25 + -3X + X2 = 49 + 2.25

Combine like terms: 49 + 2.25 = 51.25
2.25 + -3X + X2 = 51.25

Factor a perfect square on the left side:
(X + -1.5)(X + -1.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(X + -1.5) equal to 7.158910532 and -7.158910532.


Subproblem 1
X + -1.5 = 7.158910532

Simplifying
X + -1.5 = 7.158910532

Reorder the terms:
-1.5 + X = 7.158910532

Solving
-1.5 + X = 7.158910532

Solving for variable 'X'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + X = 7.158910532 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + X = 7.158910532 + 1.5
X = 7.158910532 + 1.5

Combine like terms: 7.158910532 + 1.5 = 8.658910532
X = 8.658910532

Simplifying
X = 8.658910532


Subproblem 2
X + -1.5 = -7.158910532

Simplifying
X + -1.5 = -7.158910532

Reorder the terms:
-1.5 + X = -7.158910532

Solving
-1.5 + X = -7.158910532

Solving for variable 'X'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + X = -7.158910532 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + X = -7.158910532 + 1.5
X = -7.158910532 + 1.5

Combine like terms: -7.158910532 + 1.5 = -5.658910532
X = -5.658910532

Simplifying
X = -5.658910532


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {8.658910532, -5.658910532}
Solution
X = {8.658910532, -5.658910532}

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