2x^2-62x-100=0

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Solution for 2x^2-62x-100=0 equation: 


Simplifying
2x2 + -62x + -100 = 0

Reorder the terms:
-100 + -62x + 2x2 = 0

Solving
-100 + -62x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + -31x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + -31x + x2)' equal to zero and attempt to solve:

Simplifying
-50 + -31x + x2 = 0

Solving
-50 + -31x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -31x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + -31x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -31x + x2 = 0 + 50
-31x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
-31x + x2 = 50

The x term is -31x.  Take half its coefficient (-15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
-31x + 240.25 + x2 = 50 + 240.25

Reorder the terms:
240.25 + -31x + x2 = 50 + 240.25

Combine like terms: 50 + 240.25 = 290.25
240.25 + -31x + x2 = 290.25

Factor a perfect square on the left side:
(x + -15.5)(x + -15.5) = 290.25

Calculate the square root of the right side: 17.036725037

Break this problem into two subproblems by setting 
(x + -15.5) equal to 17.036725037 and -17.036725037.


Subproblem 1
x + -15.5 = 17.036725037

Simplifying
x + -15.5 = 17.036725037

Reorder the terms:
-15.5 + x = 17.036725037

Solving
-15.5 + x = 17.036725037

Solving for variable 'x'.

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

Add '15.5' to each side of the equation.
-15.5 + 15.5 + x = 17.036725037 + 15.5

Combine like terms: -15.5 + 15.5 = 0.0
0.0 + x = 17.036725037 + 15.5
x = 17.036725037 + 15.5

Combine like terms: 17.036725037 + 15.5 = 32.536725037
x = 32.536725037

Simplifying
x = 32.536725037


Subproblem 2
x + -15.5 = -17.036725037

Simplifying
x + -15.5 = -17.036725037

Reorder the terms:
-15.5 + x = -17.036725037

Solving
-15.5 + x = -17.036725037

Solving for variable 'x'.

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

Add '15.5' to each side of the equation.
-15.5 + 15.5 + x = -17.036725037 + 15.5

Combine like terms: -15.5 + 15.5 = 0.0
0.0 + x = -17.036725037 + 15.5
x = -17.036725037 + 15.5

Combine like terms: -17.036725037 + 15.5 = -1.536725037
x = -1.536725037

Simplifying
x = -1.536725037


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {32.536725037, -1.536725037}
Solution
x = {32.536725037, -1.536725037}

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