50.3x^2-97.74x+43.173=0

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Solution for 50.3x^2-97.74x+43.173=0 equation:


Simplifying
50.3x2 + -97.74x + 43.173 = 0

Reorder the terms:
43.173 + -97.74x + 50.3x2 = 0

Solving
43.173 + -97.74x + 50.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '50.3'.
0.8583101392 + -1.943141153x + x2 = 0

Move the constant term to the right:

Add '-0.8583101392' to each side of the equation.
0.8583101392 + -1.943141153x + -0.8583101392 + x2 = 0 + -0.8583101392

Reorder the terms:
0.8583101392 + -0.8583101392 + -1.943141153x + x2 = 0 + -0.8583101392

Combine like terms: 0.8583101392 + -0.8583101392 = 0.0000000000
0.0000000000 + -1.943141153x + x2 = 0 + -0.8583101392
-1.943141153x + x2 = 0 + -0.8583101392

Combine like terms: 0 + -0.8583101392 = -0.8583101392
-1.943141153x + x2 = -0.8583101392

The x term is -1.943141153x.  Take half its coefficient (-0.9715705765).
Square it (0.9439493851) and add it to both sides.

Add '0.9439493851' to each side of the equation.
-1.943141153x + 0.9439493851 + x2 = -0.8583101392 + 0.9439493851

Reorder the terms:
0.9439493851 + -1.943141153x + x2 = -0.8583101392 + 0.9439493851

Combine like terms: -0.8583101392 + 0.9439493851 = 0.0856392459
0.9439493851 + -1.943141153x + x2 = 0.0856392459

Factor a perfect square on the left side:
(x + -0.9715705765)(x + -0.9715705765) = 0.0856392459

Calculate the square root of the right side: 0.292641839

Break this problem into two subproblems by setting 
(x + -0.9715705765) equal to 0.292641839 and -0.292641839.

Subproblem 1

x + -0.9715705765 = 0.292641839 Simplifying x + -0.9715705765 = 0.292641839 Reorder the terms: -0.9715705765 + x = 0.292641839 Solving -0.9715705765 + x = 0.292641839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9715705765' to each side of the equation. -0.9715705765 + 0.9715705765 + x = 0.292641839 + 0.9715705765 Combine like terms: -0.9715705765 + 0.9715705765 = 0.0000000000 0.0000000000 + x = 0.292641839 + 0.9715705765 x = 0.292641839 + 0.9715705765 Combine like terms: 0.292641839 + 0.9715705765 = 1.2642124155 x = 1.2642124155 Simplifying x = 1.2642124155

Subproblem 2

x + -0.9715705765 = -0.292641839 Simplifying x + -0.9715705765 = -0.292641839 Reorder the terms: -0.9715705765 + x = -0.292641839 Solving -0.9715705765 + x = -0.292641839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9715705765' to each side of the equation. -0.9715705765 + 0.9715705765 + x = -0.292641839 + 0.9715705765 Combine like terms: -0.9715705765 + 0.9715705765 = 0.0000000000 0.0000000000 + x = -0.292641839 + 0.9715705765 x = -0.292641839 + 0.9715705765 Combine like terms: -0.292641839 + 0.9715705765 = 0.6789287375 x = 0.6789287375 Simplifying x = 0.6789287375

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2642124155, 0.6789287375}

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