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Simplifying 13x2 + -20x + 1 = 0 Reorder the terms: 1 + -20x + 13x2 = 0 Solving 1 + -20x + 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'. 0.07692307692 + -1.538461538x + x2 = 0 Move the constant term to the right: Add '-0.07692307692' to each side of the equation. 0.07692307692 + -1.538461538x + -0.07692307692 + x2 = 0 + -0.07692307692 Reorder the terms: 0.07692307692 + -0.07692307692 + -1.538461538x + x2 = 0 + -0.07692307692 Combine like terms: 0.07692307692 + -0.07692307692 = 0.00000000000 0.00000000000 + -1.538461538x + x2 = 0 + -0.07692307692 -1.538461538x + x2 = 0 + -0.07692307692 Combine like terms: 0 + -0.07692307692 = -0.07692307692 -1.538461538x + x2 = -0.07692307692 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 = -0.07692307692 + 0.5917159760 Reorder the terms: 0.5917159760 + -1.538461538x + x2 = -0.07692307692 + 0.5917159760 Combine like terms: -0.07692307692 + 0.5917159760 = 0.51479289908 0.5917159760 + -1.538461538x + x2 = 0.51479289908 Factor a perfect square on the left side: (x + -0.769230769)(x + -0.769230769) = 0.51479289908 Calculate the square root of the right side: 0.717490696 Break this problem into two subproblems by setting (x + -0.769230769) equal to 0.717490696 and -0.717490696.Subproblem 1
x + -0.769230769 = 0.717490696 Simplifying x + -0.769230769 = 0.717490696 Reorder the terms: -0.769230769 + x = 0.717490696 Solving -0.769230769 + x = 0.717490696 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 = 0.717490696 + 0.769230769 Combine like terms: -0.769230769 + 0.769230769 = 0.000000000 0.000000000 + x = 0.717490696 + 0.769230769 x = 0.717490696 + 0.769230769 Combine like terms: 0.717490696 + 0.769230769 = 1.486721465 x = 1.486721465 Simplifying x = 1.486721465Subproblem 2
x + -0.769230769 = -0.717490696 Simplifying x + -0.769230769 = -0.717490696 Reorder the terms: -0.769230769 + x = -0.717490696 Solving -0.769230769 + x = -0.717490696 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 = -0.717490696 + 0.769230769 Combine like terms: -0.769230769 + 0.769230769 = 0.000000000 0.000000000 + x = -0.717490696 + 0.769230769 x = -0.717490696 + 0.769230769 Combine like terms: -0.717490696 + 0.769230769 = 0.051740073 x = 0.051740073 Simplifying x = 0.051740073Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.486721465, 0.051740073}
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