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Simplifying 1.3x2 + -11x + -100 = 0 Reorder the terms: -100 + -11x + 1.3x2 = 0 Solving -100 + -11x + 1.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.3 the coefficient of the squared term: Divide each side by '1.3'. -76.92307692 + -8.461538462x + x2 = 0 Move the constant term to the right: Add '76.92307692' to each side of the equation. -76.92307692 + -8.461538462x + 76.92307692 + x2 = 0 + 76.92307692 Reorder the terms: -76.92307692 + 76.92307692 + -8.461538462x + x2 = 0 + 76.92307692 Combine like terms: -76.92307692 + 76.92307692 = 0.00000000 0.00000000 + -8.461538462x + x2 = 0 + 76.92307692 -8.461538462x + x2 = 0 + 76.92307692 Combine like terms: 0 + 76.92307692 = 76.92307692 -8.461538462x + x2 = 76.92307692 The x term is -8.461538462x. Take half its coefficient (-4.230769231). Square it (17.89940829) and add it to both sides. Add '17.89940829' to each side of the equation. -8.461538462x + 17.89940829 + x2 = 76.92307692 + 17.89940829 Reorder the terms: 17.89940829 + -8.461538462x + x2 = 76.92307692 + 17.89940829 Combine like terms: 76.92307692 + 17.89940829 = 94.82248521 17.89940829 + -8.461538462x + x2 = 94.82248521 Factor a perfect square on the left side: (x + -4.230769231)(x + -4.230769231) = 94.82248521 Calculate the square root of the right side: 9.73768377 Break this problem into two subproblems by setting (x + -4.230769231) equal to 9.73768377 and -9.73768377.Subproblem 1
x + -4.230769231 = 9.73768377 Simplifying x + -4.230769231 = 9.73768377 Reorder the terms: -4.230769231 + x = 9.73768377 Solving -4.230769231 + x = 9.73768377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.230769231' to each side of the equation. -4.230769231 + 4.230769231 + x = 9.73768377 + 4.230769231 Combine like terms: -4.230769231 + 4.230769231 = 0.000000000 0.000000000 + x = 9.73768377 + 4.230769231 x = 9.73768377 + 4.230769231 Combine like terms: 9.73768377 + 4.230769231 = 13.968453001 x = 13.968453001 Simplifying x = 13.968453001Subproblem 2
x + -4.230769231 = -9.73768377 Simplifying x + -4.230769231 = -9.73768377 Reorder the terms: -4.230769231 + x = -9.73768377 Solving -4.230769231 + x = -9.73768377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.230769231' to each side of the equation. -4.230769231 + 4.230769231 + x = -9.73768377 + 4.230769231 Combine like terms: -4.230769231 + 4.230769231 = 0.000000000 0.000000000 + x = -9.73768377 + 4.230769231 x = -9.73768377 + 4.230769231 Combine like terms: -9.73768377 + 4.230769231 = -5.506914539 x = -5.506914539 Simplifying x = -5.506914539Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.968453001, -5.506914539}
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