52.2x^2-26.37x-15.3=0

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Solution for 52.2x^2-26.37x-15.3=0 equation:


Simplifying
52.2x2 + -26.37x + -15.3 = 0

Reorder the terms:
-15.3 + -26.37x + 52.2x2 = 0

Solving
-15.3 + -26.37x + 52.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '52.2'.
-0.2931034483 + -0.5051724138x + x2 = 0

Move the constant term to the right:

Add '0.2931034483' to each side of the equation.
-0.2931034483 + -0.5051724138x + 0.2931034483 + x2 = 0 + 0.2931034483

Reorder the terms:
-0.2931034483 + 0.2931034483 + -0.5051724138x + x2 = 0 + 0.2931034483

Combine like terms: -0.2931034483 + 0.2931034483 = 0.0000000000
0.0000000000 + -0.5051724138x + x2 = 0 + 0.2931034483
-0.5051724138x + x2 = 0 + 0.2931034483

Combine like terms: 0 + 0.2931034483 = 0.2931034483
-0.5051724138x + x2 = 0.2931034483

The x term is -0.5051724138x.  Take half its coefficient (-0.2525862069).
Square it (0.06379979192) and add it to both sides.

Add '0.06379979192' to each side of the equation.
-0.5051724138x + 0.06379979192 + x2 = 0.2931034483 + 0.06379979192

Reorder the terms:
0.06379979192 + -0.5051724138x + x2 = 0.2931034483 + 0.06379979192

Combine like terms: 0.2931034483 + 0.06379979192 = 0.35690324022
0.06379979192 + -0.5051724138x + x2 = 0.35690324022

Factor a perfect square on the left side:
(x + -0.2525862069)(x + -0.2525862069) = 0.35690324022

Calculate the square root of the right side: 0.597413793

Break this problem into two subproblems by setting 
(x + -0.2525862069) equal to 0.597413793 and -0.597413793.

Subproblem 1

x + -0.2525862069 = 0.597413793 Simplifying x + -0.2525862069 = 0.597413793 Reorder the terms: -0.2525862069 + x = 0.597413793 Solving -0.2525862069 + x = 0.597413793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2525862069' to each side of the equation. -0.2525862069 + 0.2525862069 + x = 0.597413793 + 0.2525862069 Combine like terms: -0.2525862069 + 0.2525862069 = 0.0000000000 0.0000000000 + x = 0.597413793 + 0.2525862069 x = 0.597413793 + 0.2525862069 Combine like terms: 0.597413793 + 0.2525862069 = 0.8499999999 x = 0.8499999999 Simplifying x = 0.8499999999

Subproblem 2

x + -0.2525862069 = -0.597413793 Simplifying x + -0.2525862069 = -0.597413793 Reorder the terms: -0.2525862069 + x = -0.597413793 Solving -0.2525862069 + x = -0.597413793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2525862069' to each side of the equation. -0.2525862069 + 0.2525862069 + x = -0.597413793 + 0.2525862069 Combine like terms: -0.2525862069 + 0.2525862069 = 0.0000000000 0.0000000000 + x = -0.597413793 + 0.2525862069 x = -0.597413793 + 0.2525862069 Combine like terms: -0.597413793 + 0.2525862069 = -0.3448275861 x = -0.3448275861 Simplifying x = -0.3448275861

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8499999999, -0.3448275861}

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