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Simplifying 18x2 + 4x + -10 = 5x2 + 15x Reorder the terms: -10 + 4x + 18x2 = 5x2 + 15x Reorder the terms: -10 + 4x + 18x2 = 15x + 5x2 Solving -10 + 4x + 18x2 = 15x + 5x2 Solving for variable 'x'. Reorder the terms: -10 + 4x + -15x + 18x2 + -5x2 = 15x + 5x2 + -15x + -5x2 Combine like terms: 4x + -15x = -11x -10 + -11x + 18x2 + -5x2 = 15x + 5x2 + -15x + -5x2 Combine like terms: 18x2 + -5x2 = 13x2 -10 + -11x + 13x2 = 15x + 5x2 + -15x + -5x2 Reorder the terms: -10 + -11x + 13x2 = 15x + -15x + 5x2 + -5x2 Combine like terms: 15x + -15x = 0 -10 + -11x + 13x2 = 0 + 5x2 + -5x2 -10 + -11x + 13x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -10 + -11x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.7692307692 + -0.8461538462x + x2 = 0 Move the constant term to the right: Add '0.7692307692' to each side of the equation. -0.7692307692 + -0.8461538462x + 0.7692307692 + x2 = 0 + 0.7692307692 Reorder the terms: -0.7692307692 + 0.7692307692 + -0.8461538462x + x2 = 0 + 0.7692307692 Combine like terms: -0.7692307692 + 0.7692307692 = 0.0000000000 0.0000000000 + -0.8461538462x + x2 = 0 + 0.7692307692 -0.8461538462x + x2 = 0 + 0.7692307692 Combine like terms: 0 + 0.7692307692 = 0.7692307692 -0.8461538462x + x2 = 0.7692307692 The x term is -0.8461538462x. Take half its coefficient (-0.4230769231). Square it (0.1789940829) and add it to both sides. Add '0.1789940829' to each side of the equation. -0.8461538462x + 0.1789940829 + x2 = 0.7692307692 + 0.1789940829 Reorder the terms: 0.1789940829 + -0.8461538462x + x2 = 0.7692307692 + 0.1789940829 Combine like terms: 0.7692307692 + 0.1789940829 = 0.9482248521 0.1789940829 + -0.8461538462x + x2 = 0.9482248521 Factor a perfect square on the left side: (x + -0.4230769231)(x + -0.4230769231) = 0.9482248521 Calculate the square root of the right side: 0.973768377 Break this problem into two subproblems by setting (x + -0.4230769231) equal to 0.973768377 and -0.973768377.Subproblem 1
x + -0.4230769231 = 0.973768377 Simplifying x + -0.4230769231 = 0.973768377 Reorder the terms: -0.4230769231 + x = 0.973768377 Solving -0.4230769231 + x = 0.973768377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4230769231' to each side of the equation. -0.4230769231 + 0.4230769231 + x = 0.973768377 + 0.4230769231 Combine like terms: -0.4230769231 + 0.4230769231 = 0.0000000000 0.0000000000 + x = 0.973768377 + 0.4230769231 x = 0.973768377 + 0.4230769231 Combine like terms: 0.973768377 + 0.4230769231 = 1.3968453001 x = 1.3968453001 Simplifying x = 1.3968453001Subproblem 2
x + -0.4230769231 = -0.973768377 Simplifying x + -0.4230769231 = -0.973768377 Reorder the terms: -0.4230769231 + x = -0.973768377 Solving -0.4230769231 + x = -0.973768377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4230769231' to each side of the equation. -0.4230769231 + 0.4230769231 + x = -0.973768377 + 0.4230769231 Combine like terms: -0.4230769231 + 0.4230769231 = 0.0000000000 0.0000000000 + x = -0.973768377 + 0.4230769231 x = -0.973768377 + 0.4230769231 Combine like terms: -0.973768377 + 0.4230769231 = -0.5506914539 x = -0.5506914539 Simplifying x = -0.5506914539Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3968453001, -0.5506914539}
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