4.82x^2+2x-1.80=0

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Solution for 4.82x^2+2x-1.80=0 equation:


Simplifying
4.82x2 + 2x + -1.80 = 0

Reorder the terms:
-1.80 + 2x + 4.82x2 = 0

Solving
-1.80 + 2x + 4.82x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.82'.
-0.3734439834 + 0.4149377593x + x2 = 0

Move the constant term to the right:

Add '0.3734439834' to each side of the equation.
-0.3734439834 + 0.4149377593x + 0.3734439834 + x2 = 0 + 0.3734439834

Reorder the terms:
-0.3734439834 + 0.3734439834 + 0.4149377593x + x2 = 0 + 0.3734439834

Combine like terms: -0.3734439834 + 0.3734439834 = 0.0000000000
0.0000000000 + 0.4149377593x + x2 = 0 + 0.3734439834
0.4149377593x + x2 = 0 + 0.3734439834

Combine like terms: 0 + 0.3734439834 = 0.3734439834
0.4149377593x + x2 = 0.3734439834

The x term is 0.4149377593x.  Take half its coefficient (0.2074688797).
Square it (0.04304333604) and add it to both sides.

Add '0.04304333604' to each side of the equation.
0.4149377593x + 0.04304333604 + x2 = 0.3734439834 + 0.04304333604

Reorder the terms:
0.04304333604 + 0.4149377593x + x2 = 0.3734439834 + 0.04304333604

Combine like terms: 0.3734439834 + 0.04304333604 = 0.41648731944
0.04304333604 + 0.4149377593x + x2 = 0.41648731944

Factor a perfect square on the left side:
(x + 0.2074688797)(x + 0.2074688797) = 0.41648731944

Calculate the square root of the right side: 0.645358288

Break this problem into two subproblems by setting 
(x + 0.2074688797) equal to 0.645358288 and -0.645358288.

Subproblem 1

x + 0.2074688797 = 0.645358288 Simplifying x + 0.2074688797 = 0.645358288 Reorder the terms: 0.2074688797 + x = 0.645358288 Solving 0.2074688797 + x = 0.645358288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2074688797' to each side of the equation. 0.2074688797 + -0.2074688797 + x = 0.645358288 + -0.2074688797 Combine like terms: 0.2074688797 + -0.2074688797 = 0.0000000000 0.0000000000 + x = 0.645358288 + -0.2074688797 x = 0.645358288 + -0.2074688797 Combine like terms: 0.645358288 + -0.2074688797 = 0.4378894083 x = 0.4378894083 Simplifying x = 0.4378894083

Subproblem 2

x + 0.2074688797 = -0.645358288 Simplifying x + 0.2074688797 = -0.645358288 Reorder the terms: 0.2074688797 + x = -0.645358288 Solving 0.2074688797 + x = -0.645358288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2074688797' to each side of the equation. 0.2074688797 + -0.2074688797 + x = -0.645358288 + -0.2074688797 Combine like terms: 0.2074688797 + -0.2074688797 = 0.0000000000 0.0000000000 + x = -0.645358288 + -0.2074688797 x = -0.645358288 + -0.2074688797 Combine like terms: -0.645358288 + -0.2074688797 = -0.8528271677 x = -0.8528271677 Simplifying x = -0.8528271677

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4378894083, -0.8528271677}

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