x^2+.98x+1.6083=2.91

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Solution for x^2+.98x+1.6083=2.91 equation: 


Simplifying
x2 + 0.98x + 1.6083 = 2.91

Reorder the terms:
1.6083 + 0.98x + x2 = 2.91

Solving
1.6083 + 0.98x + x2 = 2.91

Solving for variable 'x'.

Reorder the terms:
1.6083 + -2.91 + 0.98x + x2 = 2.91 + -2.91

Combine like terms: 1.6083 + -2.91 = -1.3017
-1.3017 + 0.98x + x2 = 2.91 + -2.91

Combine like terms: 2.91 + -2.91 = 0.00
-1.3017 + 0.98x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '1.3017' to each side of the equation.
-1.3017 + 0.98x + 1.3017 + x2 = 0.00 + 1.3017

Reorder the terms:
-1.3017 + 1.3017 + 0.98x + x2 = 0.00 + 1.3017

Combine like terms: -1.3017 + 1.3017 = 0.0000
0.0000 + 0.98x + x2 = 0.00 + 1.3017
0.98x + x2 = 0.00 + 1.3017

Combine like terms: 0.00 + 1.3017 = 1.3017
0.98x + x2 = 1.3017

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 = 1.3017 + 0.2401

Reorder the terms:
0.2401 + 0.98x + x2 = 1.3017 + 0.2401

Combine like terms: 1.3017 + 0.2401 = 1.5418
0.2401 + 0.98x + x2 = 1.5418

Factor a perfect square on the left side:
(x + 0.49)(x + 0.49) = 1.5418

Calculate the square root of the right side: 1.241692393

Break this problem into two subproblems by setting 
(x + 0.49) equal to 1.241692393 and -1.241692393.


Subproblem 1
x + 0.49 = 1.241692393

Simplifying
x + 0.49 = 1.241692393

Reorder the terms:
0.49 + x = 1.241692393

Solving
0.49 + x = 1.241692393

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 = 1.241692393 + -0.49

Combine like terms: 0.49 + -0.49 = 0.00
0.00 + x = 1.241692393 + -0.49
x = 1.241692393 + -0.49

Combine like terms: 1.241692393 + -0.49 = 0.751692393
x = 0.751692393

Simplifying
x = 0.751692393


Subproblem 2
x + 0.49 = -1.241692393

Simplifying
x + 0.49 = -1.241692393

Reorder the terms:
0.49 + x = -1.241692393

Solving
0.49 + x = -1.241692393

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 = -1.241692393 + -0.49

Combine like terms: 0.49 + -0.49 = 0.00
0.00 + x = -1.241692393 + -0.49
x = -1.241692393 + -0.49

Combine like terms: -1.241692393 + -0.49 = -1.731692393
x = -1.731692393

Simplifying
x = -1.731692393


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.751692393, -1.731692393}

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