4x^2+1.6x-3.2169=0

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Solution for 4x^2+1.6x-3.2169=0 equation:


Simplifying
4x2 + 1.6x + -3.2169 = 0

Reorder the terms:
-3.2169 + 1.6x + 4x2 = 0

Solving
-3.2169 + 1.6x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-0.804225 + 0.4x + x2 = 0

Move the constant term to the right:

Add '0.804225' to each side of the equation.
-0.804225 + 0.4x + 0.804225 + x2 = 0 + 0.804225

Reorder the terms:
-0.804225 + 0.804225 + 0.4x + x2 = 0 + 0.804225

Combine like terms: -0.804225 + 0.804225 = 0.000000
0.000000 + 0.4x + x2 = 0 + 0.804225
0.4x + x2 = 0 + 0.804225

Combine like terms: 0 + 0.804225 = 0.804225
0.4x + x2 = 0.804225

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 0.804225 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 0.804225 + 0.04

Combine like terms: 0.804225 + 0.04 = 0.844225
0.04 + 0.4x + x2 = 0.844225

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 0.844225

Calculate the square root of the right side: 0.918817174

Break this problem into two subproblems by setting 
(x + 0.2) equal to 0.918817174 and -0.918817174.

Subproblem 1

x + 0.2 = 0.918817174 Simplifying x + 0.2 = 0.918817174 Reorder the terms: 0.2 + x = 0.918817174 Solving 0.2 + x = 0.918817174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.918817174 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.918817174 + -0.2 x = 0.918817174 + -0.2 Combine like terms: 0.918817174 + -0.2 = 0.718817174 x = 0.718817174 Simplifying x = 0.718817174

Subproblem 2

x + 0.2 = -0.918817174 Simplifying x + 0.2 = -0.918817174 Reorder the terms: 0.2 + x = -0.918817174 Solving 0.2 + x = -0.918817174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.918817174 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.918817174 + -0.2 x = -0.918817174 + -0.2 Combine like terms: -0.918817174 + -0.2 = -1.118817174 x = -1.118817174 Simplifying x = -1.118817174

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.718817174, -1.118817174}

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