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Simplifying 13x2 + 20x + -392 = 0 Reorder the terms: -392 + 20x + 13x2 = 0 Solving -392 + 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'. -30.15384615 + 1.538461538x + x2 = 0 Move the constant term to the right: Add '30.15384615' to each side of the equation. -30.15384615 + 1.538461538x + 30.15384615 + x2 = 0 + 30.15384615 Reorder the terms: -30.15384615 + 30.15384615 + 1.538461538x + x2 = 0 + 30.15384615 Combine like terms: -30.15384615 + 30.15384615 = 0.00000000 0.00000000 + 1.538461538x + x2 = 0 + 30.15384615 1.538461538x + x2 = 0 + 30.15384615 Combine like terms: 0 + 30.15384615 = 30.15384615 1.538461538x + x2 = 30.15384615 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 = 30.15384615 + 0.5917159760 Reorder the terms: 0.5917159760 + 1.538461538x + x2 = 30.15384615 + 0.5917159760 Combine like terms: 30.15384615 + 0.5917159760 = 30.745562126 0.5917159760 + 1.538461538x + x2 = 30.745562126 Factor a perfect square on the left side: (x + 0.769230769)(x + 0.769230769) = 30.745562126 Calculate the square root of the right side: 5.544868089 Break this problem into two subproblems by setting (x + 0.769230769) equal to 5.544868089 and -5.544868089.Subproblem 1
x + 0.769230769 = 5.544868089 Simplifying x + 0.769230769 = 5.544868089 Reorder the terms: 0.769230769 + x = 5.544868089 Solving 0.769230769 + x = 5.544868089 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 = 5.544868089 + -0.769230769 Combine like terms: 0.769230769 + -0.769230769 = 0.000000000 0.000000000 + x = 5.544868089 + -0.769230769 x = 5.544868089 + -0.769230769 Combine like terms: 5.544868089 + -0.769230769 = 4.77563732 x = 4.77563732 Simplifying x = 4.77563732Subproblem 2
x + 0.769230769 = -5.544868089 Simplifying x + 0.769230769 = -5.544868089 Reorder the terms: 0.769230769 + x = -5.544868089 Solving 0.769230769 + x = -5.544868089 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 = -5.544868089 + -0.769230769 Combine like terms: 0.769230769 + -0.769230769 = 0.000000000 0.000000000 + x = -5.544868089 + -0.769230769 x = -5.544868089 + -0.769230769 Combine like terms: -5.544868089 + -0.769230769 = -6.314098858 x = -6.314098858 Simplifying x = -6.314098858Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.77563732, -6.314098858}
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