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Simplifying -0.111x2 + 4x + -36 = 0 Reorder the terms: -36 + 4x + -0.111x2 = 0 Solving -36 + 4x + -0.111x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.111 the coefficient of the squared term: Divide each side by '-0.111'. 324.3243243 + -36.03603604x + x2 = 0 Move the constant term to the right: Add '-324.3243243' to each side of the equation. 324.3243243 + -36.03603604x + -324.3243243 + x2 = 0 + -324.3243243 Reorder the terms: 324.3243243 + -324.3243243 + -36.03603604x + x2 = 0 + -324.3243243 Combine like terms: 324.3243243 + -324.3243243 = 0.0000000 0.0000000 + -36.03603604x + x2 = 0 + -324.3243243 -36.03603604x + x2 = 0 + -324.3243243 Combine like terms: 0 + -324.3243243 = -324.3243243 -36.03603604x + x2 = -324.3243243 The x term is -36.03603604x. Take half its coefficient (-18.01801802). Square it (324.6489734) and add it to both sides. Add '324.6489734' to each side of the equation. -36.03603604x + 324.6489734 + x2 = -324.3243243 + 324.6489734 Reorder the terms: 324.6489734 + -36.03603604x + x2 = -324.3243243 + 324.6489734 Combine like terms: -324.3243243 + 324.6489734 = 0.3246491 324.6489734 + -36.03603604x + x2 = 0.3246491 Factor a perfect square on the left side: (x + -18.01801802)(x + -18.01801802) = 0.3246491 Calculate the square root of the right side: 0.56977987 Break this problem into two subproblems by setting (x + -18.01801802) equal to 0.56977987 and -0.56977987.Subproblem 1
x + -18.01801802 = 0.56977987 Simplifying x + -18.01801802 = 0.56977987 Reorder the terms: -18.01801802 + x = 0.56977987 Solving -18.01801802 + x = 0.56977987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.01801802' to each side of the equation. -18.01801802 + 18.01801802 + x = 0.56977987 + 18.01801802 Combine like terms: -18.01801802 + 18.01801802 = 0.00000000 0.00000000 + x = 0.56977987 + 18.01801802 x = 0.56977987 + 18.01801802 Combine like terms: 0.56977987 + 18.01801802 = 18.58779789 x = 18.58779789 Simplifying x = 18.58779789Subproblem 2
x + -18.01801802 = -0.56977987 Simplifying x + -18.01801802 = -0.56977987 Reorder the terms: -18.01801802 + x = -0.56977987 Solving -18.01801802 + x = -0.56977987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.01801802' to each side of the equation. -18.01801802 + 18.01801802 + x = -0.56977987 + 18.01801802 Combine like terms: -18.01801802 + 18.01801802 = 0.00000000 0.00000000 + x = -0.56977987 + 18.01801802 x = -0.56977987 + 18.01801802 Combine like terms: -0.56977987 + 18.01801802 = 17.44823815 x = 17.44823815 Simplifying x = 17.44823815Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.58779789, 17.44823815}
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