x^2-6x-97=0

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Solution for x^2-6x-97=0 equation: 


Simplifying
x2 + -6x + -97 = 0

Reorder the terms:
-97 + -6x + x2 = 0

Solving
-97 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '97' to each side of the equation.
-97 + -6x + 97 + x2 = 0 + 97

Reorder the terms:
-97 + 97 + -6x + x2 = 0 + 97

Combine like terms: -97 + 97 = 0
0 + -6x + x2 = 0 + 97
-6x + x2 = 0 + 97

Combine like terms: 0 + 97 = 97
-6x + x2 = 97

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 97 + 9

Reorder the terms:
9 + -6x + x2 = 97 + 9

Combine like terms: 97 + 9 = 106
9 + -6x + x2 = 106

Factor a perfect square on the left side:
(x + -3)(x + -3) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + -3) equal to 10.295630141 and -10.295630141.


Subproblem 1
x + -3 = 10.295630141

Simplifying
x + -3 = 10.295630141

Reorder the terms:
-3 + x = 10.295630141

Solving
-3 + x = 10.295630141

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 10.295630141 + 3

Combine like terms: -3 + 3 = 0
0 + x = 10.295630141 + 3
x = 10.295630141 + 3

Combine like terms: 10.295630141 + 3 = 13.295630141
x = 13.295630141

Simplifying
x = 13.295630141


Subproblem 2
x + -3 = -10.295630141

Simplifying
x + -3 = -10.295630141

Reorder the terms:
-3 + x = -10.295630141

Solving
-3 + x = -10.295630141

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -10.295630141 + 3

Combine like terms: -3 + 3 = 0
0 + x = -10.295630141 + 3
x = -10.295630141 + 3

Combine like terms: -10.295630141 + 3 = -7.295630141
x = -7.295630141

Simplifying
x = -7.295630141


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.295630141, -7.295630141}

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