X^2-10X-91=0

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Solution for X^2-10X-91=0 equation: 


Simplifying
X2 + -10X + -91 = 0

Reorder the terms:
-91 + -10X + X2 = 0

Solving
-91 + -10X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '91' to each side of the equation.
-91 + -10X + 91 + X2 = 0 + 91

Reorder the terms:
-91 + 91 + -10X + X2 = 0 + 91

Combine like terms: -91 + 91 = 0
0 + -10X + X2 = 0 + 91
-10X + X2 = 0 + 91

Combine like terms: 0 + 91 = 91
-10X + X2 = 91

The X term is -10X.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10X + 25 + X2 = 91 + 25

Reorder the terms:
25 + -10X + X2 = 91 + 25

Combine like terms: 91 + 25 = 116
25 + -10X + X2 = 116

Factor a perfect square on the left side:
(X + -5)(X + -5) = 116

Calculate the square root of the right side: 10.770329614

Break this problem into two subproblems by setting 
(X + -5) equal to 10.770329614 and -10.770329614.


Subproblem 1
X + -5 = 10.770329614

Simplifying
X + -5 = 10.770329614

Reorder the terms:
-5 + X = 10.770329614

Solving
-5 + X = 10.770329614

Solving for variable 'X'.

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

Add '5' to each side of the equation.
-5 + 5 + X = 10.770329614 + 5

Combine like terms: -5 + 5 = 0
0 + X = 10.770329614 + 5
X = 10.770329614 + 5

Combine like terms: 10.770329614 + 5 = 15.770329614
X = 15.770329614

Simplifying
X = 15.770329614


Subproblem 2
X + -5 = -10.770329614

Simplifying
X + -5 = -10.770329614

Reorder the terms:
-5 + X = -10.770329614

Solving
-5 + X = -10.770329614

Solving for variable 'X'.

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

Add '5' to each side of the equation.
-5 + 5 + X = -10.770329614 + 5

Combine like terms: -5 + 5 = 0
0 + X = -10.770329614 + 5
X = -10.770329614 + 5

Combine like terms: -10.770329614 + 5 = -5.770329614
X = -5.770329614

Simplifying
X = -5.770329614


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {15.770329614, -5.770329614}

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