0.22+(0.98x)-(x^2)=0

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Solution for 0.22+(0.98x)-(x^2)=0 equation: 


Simplifying
0.22 + (0.98x) + -1(x2) = 0

Solving
0.22 + (0.98x) + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.22 + (-0.98x) + x2 = 0

Move the constant term to the right:

Add '0.22' to each side of the equation.
-0.22 + (-0.98x) + 0.22 + x2 = 0 + 0.22

Reorder the terms:
-0.22 + 0.22 + (-0.98x) + x2 = 0 + 0.22

Combine like terms: -0.22 + 0.22 = 0.00
0.00 + (-0.98x) + x2 = 0 + 0.22
(-0.98x) + x2 = 0 + 0.22

Combine like terms: 0 + 0.22 = 0.22
(-0.98x) + x2 = 0.22

The x term is (-0.98x).  Take half its coefficient (-0.49).
Square it (0.2401) and add it to both sides.

Add '0.2401' to each side of the equation.
(-0.98x) + 0.2401 + x2 = 0.22 + 0.2401

Reorder the terms:
0.2401 + (-0.98x) + x2 = 0.22 + 0.2401

Combine like terms: 0.22 + 0.2401 = 0.4601
0.2401 + (-0.98x) + x2 = 0.4601

Factor a perfect square on the left side:
(x + -0.49)(x + -0.49) = 0.4601

Calculate the square root of the right side: 0.678306715

Break this problem into two subproblems by setting 
(x + -0.49) equal to 0.678306715 and -0.678306715.


Subproblem 1
x + -0.49 = 0.678306715

Simplifying
x + -0.49 = 0.678306715

Reorder the terms:
-0.49 + x = 0.678306715

Solving
-0.49 + x = 0.678306715

Solving for variable 'x'.

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

Add '0.49' to each side of the equation.
-0.49 + 0.49 + x = 0.678306715 + 0.49

Combine like terms: -0.49 + 0.49 = 0.00
0.00 + x = 0.678306715 + 0.49
x = 0.678306715 + 0.49

Combine like terms: 0.678306715 + 0.49 = 1.168306715
x = 1.168306715

Simplifying
x = 1.168306715


Subproblem 2
x + -0.49 = -0.678306715

Simplifying
x + -0.49 = -0.678306715

Reorder the terms:
-0.49 + x = -0.678306715

Solving
-0.49 + x = -0.678306715

Solving for variable 'x'.

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

Add '0.49' to each side of the equation.
-0.49 + 0.49 + x = -0.678306715 + 0.49

Combine like terms: -0.49 + 0.49 = 0.00
0.00 + x = -0.678306715 + 0.49
x = -0.678306715 + 0.49

Combine like terms: -0.678306715 + 0.49 = -0.188306715
x = -0.188306715

Simplifying
x = -0.188306715


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.168306715, -0.188306715}

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