x^2+1.6x-14.57=0

Solution for x^2+1.6x-14.57=0 equation:

Simplifying
x2 + 1.6x + -14.57 = 0

Reorder the terms:
-14.57 + 1.6x + x2 = 0

Solving
-14.57 + 1.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '14.57' to each side of the equation.
-14.57 + 1.6x + 14.57 + x2 = 0 + 14.57

Reorder the terms:
-14.57 + 14.57 + 1.6x + x2 = 0 + 14.57

Combine like terms: -14.57 + 14.57 = 0.00
0.00 + 1.6x + x2 = 0 + 14.57
1.6x + x2 = 0 + 14.57

Combine like terms: 0 + 14.57 = 14.57
1.6x + x2 = 14.57

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 14.57 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 14.57 + 0.64

Combine like terms: 14.57 + 0.64 = 15.21
0.64 + 1.6x + x2 = 15.21

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 15.21

Calculate the square root of the right side: 3.9

Break this problem into two subproblems by setting 
(x + 0.8) equal to 3.9 and -3.9.

Subproblem 1
x + 0.8 = 3.9

Simplifying
x + 0.8 = 3.9

Reorder the terms:
0.8 + x = 3.9

Solving
0.8 + x = 3.9

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = 3.9 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = 3.9 + -0.8
x = 3.9 + -0.8

Combine like terms: 3.9 + -0.8 = 3.1
x = 3.1

Simplifying
x = 3.1

Subproblem 2
x + 0.8 = -3.9

Simplifying
x + 0.8 = -3.9

Reorder the terms:
0.8 + x = -3.9

Solving
0.8 + x = -3.9

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = -3.9 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = -3.9 + -0.8
x = -3.9 + -0.8

Combine like terms: -3.9 + -0.8 = -4.7
x = -4.7

Simplifying
x = -4.7

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.1, -4.7}