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Simplifying 26x2 + -40x + 12 = 0 Reorder the terms: 12 + -40x + 26x2 = 0 Solving 12 + -40x + 26x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -20x + 13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -20x + 13x2)' equal to zero and attempt to solve: Simplifying 6 + -20x + 13x2 = 0 Solving 6 + -20x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.4615384615 + -1.538461538x + x2 = 0 Move the constant term to the right: Add '-0.4615384615' to each side of the equation. 0.4615384615 + -1.538461538x + -0.4615384615 + x2 = 0 + -0.4615384615 Reorder the terms: 0.4615384615 + -0.4615384615 + -1.538461538x + x2 = 0 + -0.4615384615 Combine like terms: 0.4615384615 + -0.4615384615 = 0.0000000000 0.0000000000 + -1.538461538x + x2 = 0 + -0.4615384615 -1.538461538x + x2 = 0 + -0.4615384615 Combine like terms: 0 + -0.4615384615 = -0.4615384615 -1.538461538x + x2 = -0.4615384615 The x term is -1.538461538x. Take half its coefficient (-0.769230769). Square it (0.5917159760) and add it to both sides. Add '0.5917159760' to each side of the equation. -1.538461538x + 0.5917159760 + x2 = -0.4615384615 + 0.5917159760 Reorder the terms: 0.5917159760 + -1.538461538x + x2 = -0.4615384615 + 0.5917159760 Combine like terms: -0.4615384615 + 0.5917159760 = 0.1301775145 0.5917159760 + -1.538461538x + x2 = 0.1301775145 Factor a perfect square on the left side: (x + -0.769230769)(x + -0.769230769) = 0.1301775145 Calculate the square root of the right side: 0.360801212 Break this problem into two subproblems by setting (x + -0.769230769) equal to 0.360801212 and -0.360801212.Subproblem 1
x + -0.769230769 = 0.360801212 Simplifying x + -0.769230769 = 0.360801212 Reorder the terms: -0.769230769 + x = 0.360801212 Solving -0.769230769 + x = 0.360801212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.769230769' to each side of the equation. -0.769230769 + 0.769230769 + x = 0.360801212 + 0.769230769 Combine like terms: -0.769230769 + 0.769230769 = 0.000000000 0.000000000 + x = 0.360801212 + 0.769230769 x = 0.360801212 + 0.769230769 Combine like terms: 0.360801212 + 0.769230769 = 1.130031981 x = 1.130031981 Simplifying x = 1.130031981Subproblem 2
x + -0.769230769 = -0.360801212 Simplifying x + -0.769230769 = -0.360801212 Reorder the terms: -0.769230769 + x = -0.360801212 Solving -0.769230769 + x = -0.360801212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.769230769' to each side of the equation. -0.769230769 + 0.769230769 + x = -0.360801212 + 0.769230769 Combine like terms: -0.769230769 + 0.769230769 = 0.000000000 0.000000000 + x = -0.360801212 + 0.769230769 x = -0.360801212 + 0.769230769 Combine like terms: -0.360801212 + 0.769230769 = 0.408429557 x = 0.408429557 Simplifying x = 0.408429557Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.130031981, 0.408429557}Solution
x = {1.130031981, 0.408429557}
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