0.02-0.04x-0.98x^2=0

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Solution for 0.02-0.04x-0.98x^2=0 equation: 


Simplifying
0.02 + -0.04x + -0.98x2 = 0

Solving
0.02 + -0.04x + -0.98x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.98 the coefficient of the squared term: 

Divide each side by '-0.98'.
-0.02040816327 + 0.04081632653x + x2 = 0

Move the constant term to the right:

Add '0.02040816327' to each side of the equation.
-0.02040816327 + 0.04081632653x + 0.02040816327 + x2 = 0 + 0.02040816327

Reorder the terms:
-0.02040816327 + 0.02040816327 + 0.04081632653x + x2 = 0 + 0.02040816327

Combine like terms: -0.02040816327 + 0.02040816327 = 0.00000000000
0.00000000000 + 0.04081632653x + x2 = 0 + 0.02040816327
0.04081632653x + x2 = 0 + 0.02040816327

Combine like terms: 0 + 0.02040816327 = 0.02040816327
0.04081632653x + x2 = 0.02040816327

The x term is 0.04081632653x.  Take half its coefficient (0.02040816327).
Square it (0.0004164931281) and add it to both sides.

Add '0.0004164931281' to each side of the equation.
0.04081632653x + 0.0004164931281 + x2 = 0.02040816327 + 0.0004164931281

Reorder the terms:
0.0004164931281 + 0.04081632653x + x2 = 0.02040816327 + 0.0004164931281

Combine like terms: 0.02040816327 + 0.0004164931281 = 0.0208246563981
0.0004164931281 + 0.04081632653x + x2 = 0.0208246563981

Factor a perfect square on the left side:
(x + 0.02040816327)(x + 0.02040816327) = 0.0208246563981

Calculate the square root of the right side: 0.144307506

Break this problem into two subproblems by setting 
(x + 0.02040816327) equal to 0.144307506 and -0.144307506.


Subproblem 1
x + 0.02040816327 = 0.144307506

Simplifying
x + 0.02040816327 = 0.144307506

Reorder the terms:
0.02040816327 + x = 0.144307506

Solving
0.02040816327 + x = 0.144307506

Solving for variable 'x'.

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

Add '-0.02040816327' to each side of the equation.
0.02040816327 + -0.02040816327 + x = 0.144307506 + -0.02040816327

Combine like terms: 0.02040816327 + -0.02040816327 = 0.00000000000
0.00000000000 + x = 0.144307506 + -0.02040816327
x = 0.144307506 + -0.02040816327

Combine like terms: 0.144307506 + -0.02040816327 = 0.12389934273
x = 0.12389934273

Simplifying
x = 0.12389934273


Subproblem 2
x + 0.02040816327 = -0.144307506

Simplifying
x + 0.02040816327 = -0.144307506

Reorder the terms:
0.02040816327 + x = -0.144307506

Solving
0.02040816327 + x = -0.144307506

Solving for variable 'x'.

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

Add '-0.02040816327' to each side of the equation.
0.02040816327 + -0.02040816327 + x = -0.144307506 + -0.02040816327

Combine like terms: 0.02040816327 + -0.02040816327 = 0.00000000000
0.00000000000 + x = -0.144307506 + -0.02040816327
x = -0.144307506 + -0.02040816327

Combine like terms: -0.144307506 + -0.02040816327 = -0.16471566927
x = -0.16471566927

Simplifying
x = -0.16471566927


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.12389934273, -0.16471566927}

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