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Simplifying 15x2 + -64x + -3600 = 0 Reorder the terms: -3600 + -64x + 15x2 = 0 Solving -3600 + -64x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -240 + -4.266666667x + x2 = 0 Move the constant term to the right: Add '240' to each side of the equation. -240 + -4.266666667x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + -4.266666667x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + -4.266666667x + x2 = 0 + 240 -4.266666667x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 -4.266666667x + x2 = 240 The x term is -4.266666667x. Take half its coefficient (-2.133333334). Square it (4.551111114) and add it to both sides. Add '4.551111114' to each side of the equation. -4.266666667x + 4.551111114 + x2 = 240 + 4.551111114 Reorder the terms: 4.551111114 + -4.266666667x + x2 = 240 + 4.551111114 Combine like terms: 240 + 4.551111114 = 244.551111114 4.551111114 + -4.266666667x + x2 = 244.551111114 Factor a perfect square on the left side: (x + -2.133333334)(x + -2.133333334) = 244.551111114 Calculate the square root of the right side: 15.638130039 Break this problem into two subproblems by setting (x + -2.133333334) equal to 15.638130039 and -15.638130039.Subproblem 1
x + -2.133333334 = 15.638130039 Simplifying x + -2.133333334 = 15.638130039 Reorder the terms: -2.133333334 + x = 15.638130039 Solving -2.133333334 + x = 15.638130039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.133333334' to each side of the equation. -2.133333334 + 2.133333334 + x = 15.638130039 + 2.133333334 Combine like terms: -2.133333334 + 2.133333334 = 0.000000000 0.000000000 + x = 15.638130039 + 2.133333334 x = 15.638130039 + 2.133333334 Combine like terms: 15.638130039 + 2.133333334 = 17.771463373 x = 17.771463373 Simplifying x = 17.771463373Subproblem 2
x + -2.133333334 = -15.638130039 Simplifying x + -2.133333334 = -15.638130039 Reorder the terms: -2.133333334 + x = -15.638130039 Solving -2.133333334 + x = -15.638130039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.133333334' to each side of the equation. -2.133333334 + 2.133333334 + x = -15.638130039 + 2.133333334 Combine like terms: -2.133333334 + 2.133333334 = 0.000000000 0.000000000 + x = -15.638130039 + 2.133333334 x = -15.638130039 + 2.133333334 Combine like terms: -15.638130039 + 2.133333334 = -13.504796705 x = -13.504796705 Simplifying x = -13.504796705Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.771463373, -13.504796705}
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