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Simplifying 13x2 + -12x + 2 = 0 Reorder the terms: 2 + -12x + 13x2 = 0 Solving 2 + -12x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.1538461538 + -0.9230769231x + x2 = 0 Move the constant term to the right: Add '-0.1538461538' to each side of the equation. 0.1538461538 + -0.9230769231x + -0.1538461538 + x2 = 0 + -0.1538461538 Reorder the terms: 0.1538461538 + -0.1538461538 + -0.9230769231x + x2 = 0 + -0.1538461538 Combine like terms: 0.1538461538 + -0.1538461538 = 0.0000000000 0.0000000000 + -0.9230769231x + x2 = 0 + -0.1538461538 -0.9230769231x + x2 = 0 + -0.1538461538 Combine like terms: 0 + -0.1538461538 = -0.1538461538 -0.9230769231x + x2 = -0.1538461538 The x term is -0.9230769231x. Take half its coefficient (-0.4615384616). Square it (0.2130177515) and add it to both sides. Add '0.2130177515' to each side of the equation. -0.9230769231x + 0.2130177515 + x2 = -0.1538461538 + 0.2130177515 Reorder the terms: 0.2130177515 + -0.9230769231x + x2 = -0.1538461538 + 0.2130177515 Combine like terms: -0.1538461538 + 0.2130177515 = 0.0591715977 0.2130177515 + -0.9230769231x + x2 = 0.0591715977 Factor a perfect square on the left side: (x + -0.4615384616)(x + -0.4615384616) = 0.0591715977 Calculate the square root of the right side: 0.243252128 Break this problem into two subproblems by setting (x + -0.4615384616) equal to 0.243252128 and -0.243252128.Subproblem 1
x + -0.4615384616 = 0.243252128 Simplifying x + -0.4615384616 = 0.243252128 Reorder the terms: -0.4615384616 + x = 0.243252128 Solving -0.4615384616 + x = 0.243252128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4615384616' to each side of the equation. -0.4615384616 + 0.4615384616 + x = 0.243252128 + 0.4615384616 Combine like terms: -0.4615384616 + 0.4615384616 = 0.0000000000 0.0000000000 + x = 0.243252128 + 0.4615384616 x = 0.243252128 + 0.4615384616 Combine like terms: 0.243252128 + 0.4615384616 = 0.7047905896 x = 0.7047905896 Simplifying x = 0.7047905896Subproblem 2
x + -0.4615384616 = -0.243252128 Simplifying x + -0.4615384616 = -0.243252128 Reorder the terms: -0.4615384616 + x = -0.243252128 Solving -0.4615384616 + x = -0.243252128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4615384616' to each side of the equation. -0.4615384616 + 0.4615384616 + x = -0.243252128 + 0.4615384616 Combine like terms: -0.4615384616 + 0.4615384616 = 0.0000000000 0.0000000000 + x = -0.243252128 + 0.4615384616 x = -0.243252128 + 0.4615384616 Combine like terms: -0.243252128 + 0.4615384616 = 0.2182863336 x = 0.2182863336 Simplifying x = 0.2182863336Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7047905896, 0.2182863336}
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