x^2+0.6x-0.91=0

Solution for x^2+0.6x-0.91=0 equation:

Simplifying
x2 + 0.6x + -0.91 = 0

Reorder the terms:
-0.91 + 0.6x + x2 = 0

Solving
-0.91 + 0.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.91' to each side of the equation.
-0.91 + 0.6x + 0.91 + x2 = 0 + 0.91

Reorder the terms:
-0.91 + 0.91 + 0.6x + x2 = 0 + 0.91

Combine like terms: -0.91 + 0.91 = 0.00
0.00 + 0.6x + x2 = 0 + 0.91
0.6x + x2 = 0 + 0.91

Combine like terms: 0 + 0.91 = 0.91
0.6x + x2 = 0.91

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 0.91 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 0.91 + 0.09

Combine like terms: 0.91 + 0.09 = 1
0.09 + 0.6x + x2 = 1

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + 0.3) equal to 1 and -1.

Subproblem 1
x + 0.3 = 1

Simplifying
x + 0.3 = 1

Reorder the terms:
0.3 + x = 1

Solving
0.3 + x = 1

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = 1 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 1 + -0.3
x = 1 + -0.3

Combine like terms: 1 + -0.3 = 0.7
x = 0.7

Simplifying
x = 0.7

Subproblem 2
x + 0.3 = -1

Simplifying
x + 0.3 = -1

Reorder the terms:
0.3 + x = -1

Solving
0.3 + x = -1

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = -1 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -1 + -0.3
x = -1 + -0.3

Combine like terms: -1 + -0.3 = -1.3
x = -1.3

Simplifying
x = -1.3

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7, -1.3}