x^2+6x-97=0

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 = 7.295630141
x = 7.295630141

Simplifying
x = 7.295630141

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 = -13.295630141
x = -13.295630141

Simplifying
x = -13.295630141

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