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Simplifying 24x2 + -73x + 11.5 = 0 Reorder the terms: 11.5 + -73x + 24x2 = 0 Solving 11.5 + -73x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.4791666667 + -3.041666667x + x2 = 0 Move the constant term to the right: Add '-0.4791666667' to each side of the equation. 0.4791666667 + -3.041666667x + -0.4791666667 + x2 = 0 + -0.4791666667 Reorder the terms: 0.4791666667 + -0.4791666667 + -3.041666667x + x2 = 0 + -0.4791666667 Combine like terms: 0.4791666667 + -0.4791666667 = 0.0000000000 0.0000000000 + -3.041666667x + x2 = 0 + -0.4791666667 -3.041666667x + x2 = 0 + -0.4791666667 Combine like terms: 0 + -0.4791666667 = -0.4791666667 -3.041666667x + x2 = -0.4791666667 The x term is -3.041666667x. Take half its coefficient (-1.520833334). Square it (2.312934030) and add it to both sides. Add '2.312934030' to each side of the equation. -3.041666667x + 2.312934030 + x2 = -0.4791666667 + 2.312934030 Reorder the terms: 2.312934030 + -3.041666667x + x2 = -0.4791666667 + 2.312934030 Combine like terms: -0.4791666667 + 2.312934030 = 1.8337673633 2.312934030 + -3.041666667x + x2 = 1.8337673633 Factor a perfect square on the left side: (x + -1.520833334)(x + -1.520833334) = 1.8337673633 Calculate the square root of the right side: 1.354166667 Break this problem into two subproblems by setting (x + -1.520833334) equal to 1.354166667 and -1.354166667.Subproblem 1
x + -1.520833334 = 1.354166667 Simplifying x + -1.520833334 = 1.354166667 Reorder the terms: -1.520833334 + x = 1.354166667 Solving -1.520833334 + x = 1.354166667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.520833334' to each side of the equation. -1.520833334 + 1.520833334 + x = 1.354166667 + 1.520833334 Combine like terms: -1.520833334 + 1.520833334 = 0.000000000 0.000000000 + x = 1.354166667 + 1.520833334 x = 1.354166667 + 1.520833334 Combine like terms: 1.354166667 + 1.520833334 = 2.875000001 x = 2.875000001 Simplifying x = 2.875000001Subproblem 2
x + -1.520833334 = -1.354166667 Simplifying x + -1.520833334 = -1.354166667 Reorder the terms: -1.520833334 + x = -1.354166667 Solving -1.520833334 + x = -1.354166667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.520833334' to each side of the equation. -1.520833334 + 1.520833334 + x = -1.354166667 + 1.520833334 Combine like terms: -1.520833334 + 1.520833334 = 0.000000000 0.000000000 + x = -1.354166667 + 1.520833334 x = -1.354166667 + 1.520833334 Combine like terms: -1.354166667 + 1.520833334 = 0.166666667 x = 0.166666667 Simplifying x = 0.166666667Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.875000001, 0.166666667}
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