5.8*x^2-3.4*x-300=0

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Solution for 5.8*x^2-3.4*x-300=0 equation: 


Simplifying
5.8x2 + -3.4x + -300 = 0

Reorder the terms:
-300 + -3.4x + 5.8x2 = 0

Solving
-300 + -3.4x + 5.8x2 = 0

Solving for variable 'x'.

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

Divide each side by '5.8'.
-51.72413793 + -0.5862068966x + x2 = 0

Move the constant term to the right:

Add '51.72413793' to each side of the equation.
-51.72413793 + -0.5862068966x + 51.72413793 + x2 = 0 + 51.72413793

Reorder the terms:
-51.72413793 + 51.72413793 + -0.5862068966x + x2 = 0 + 51.72413793

Combine like terms: -51.72413793 + 51.72413793 = 0.00000000
0.00000000 + -0.5862068966x + x2 = 0 + 51.72413793
-0.5862068966x + x2 = 0 + 51.72413793

Combine like terms: 0 + 51.72413793 = 51.72413793
-0.5862068966x + x2 = 51.72413793

The x term is -0.5862068966x.  Take half its coefficient (-0.2931034483).
Square it (0.08590963141) and add it to both sides.

Add '0.08590963141' to each side of the equation.
-0.5862068966x + 0.08590963141 + x2 = 51.72413793 + 0.08590963141

Reorder the terms:
0.08590963141 + -0.5862068966x + x2 = 51.72413793 + 0.08590963141

Combine like terms: 51.72413793 + 0.08590963141 = 51.81004756141
0.08590963141 + -0.5862068966x + x2 = 51.81004756141

Factor a perfect square on the left side:
(x + -0.2931034483)(x + -0.2931034483) = 51.81004756141

Calculate the square root of the right side: 7.197919669

Break this problem into two subproblems by setting 
(x + -0.2931034483) equal to 7.197919669 and -7.197919669.


Subproblem 1
x + -0.2931034483 = 7.197919669

Simplifying
x + -0.2931034483 = 7.197919669

Reorder the terms:
-0.2931034483 + x = 7.197919669

Solving
-0.2931034483 + x = 7.197919669

Solving for variable 'x'.

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

Add '0.2931034483' to each side of the equation.
-0.2931034483 + 0.2931034483 + x = 7.197919669 + 0.2931034483

Combine like terms: -0.2931034483 + 0.2931034483 = 0.0000000000
0.0000000000 + x = 7.197919669 + 0.2931034483
x = 7.197919669 + 0.2931034483

Combine like terms: 7.197919669 + 0.2931034483 = 7.4910231173
x = 7.4910231173

Simplifying
x = 7.4910231173


Subproblem 2
x + -0.2931034483 = -7.197919669

Simplifying
x + -0.2931034483 = -7.197919669

Reorder the terms:
-0.2931034483 + x = -7.197919669

Solving
-0.2931034483 + x = -7.197919669

Solving for variable 'x'.

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

Add '0.2931034483' to each side of the equation.
-0.2931034483 + 0.2931034483 + x = -7.197919669 + 0.2931034483

Combine like terms: -0.2931034483 + 0.2931034483 = 0.0000000000
0.0000000000 + x = -7.197919669 + 0.2931034483
x = -7.197919669 + 0.2931034483

Combine like terms: -7.197919669 + 0.2931034483 = -6.9048162207
x = -6.9048162207

Simplifying
x = -6.9048162207


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.4910231173, -6.9048162207}

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