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Simplifying 15x2 + -64x + 48 = 0 Reorder the terms: 48 + -64x + 15x2 = 0 Solving 48 + -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'. 3.2 + -4.266666667x + x2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -4.266666667x + -3.2 + x2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -4.266666667x + x2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -4.266666667x + x2 = 0 + -3.2 -4.266666667x + x2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -4.266666667x + x2 = -3.2 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 = -3.2 + 4.551111114 Reorder the terms: 4.551111114 + -4.266666667x + x2 = -3.2 + 4.551111114 Combine like terms: -3.2 + 4.551111114 = 1.351111114 4.551111114 + -4.266666667x + x2 = 1.351111114 Factor a perfect square on the left side: (x + -2.133333334)(x + -2.133333334) = 1.351111114 Calculate the square root of the right side: 1.162373053 Break this problem into two subproblems by setting (x + -2.133333334) equal to 1.162373053 and -1.162373053.Subproblem 1
x + -2.133333334 = 1.162373053 Simplifying x + -2.133333334 = 1.162373053 Reorder the terms: -2.133333334 + x = 1.162373053 Solving -2.133333334 + x = 1.162373053 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 = 1.162373053 + 2.133333334 Combine like terms: -2.133333334 + 2.133333334 = 0.000000000 0.000000000 + x = 1.162373053 + 2.133333334 x = 1.162373053 + 2.133333334 Combine like terms: 1.162373053 + 2.133333334 = 3.295706387 x = 3.295706387 Simplifying x = 3.295706387Subproblem 2
x + -2.133333334 = -1.162373053 Simplifying x + -2.133333334 = -1.162373053 Reorder the terms: -2.133333334 + x = -1.162373053 Solving -2.133333334 + x = -1.162373053 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 = -1.162373053 + 2.133333334 Combine like terms: -2.133333334 + 2.133333334 = 0.000000000 0.000000000 + x = -1.162373053 + 2.133333334 x = -1.162373053 + 2.133333334 Combine like terms: -1.162373053 + 2.133333334 = 0.970960281 x = 0.970960281 Simplifying x = 0.970960281Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.295706387, 0.970960281}
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