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Simplifying -1x(13 + -14x) = -3(5 + -9x) + 2 (13 * -1x + -14x * -1x) = -3(5 + -9x) + 2 (-13x + 14x2) = -3(5 + -9x) + 2 -13x + 14x2 = (5 * -3 + -9x * -3) + 2 -13x + 14x2 = (-15 + 27x) + 2 Reorder the terms: -13x + 14x2 = -15 + 2 + 27x Combine like terms: -15 + 2 = -13 -13x + 14x2 = -13 + 27x Solving -13x + 14x2 = -13 + 27x Solving for variable 'x'. Reorder the terms: 13 + -13x + -27x + 14x2 = -13 + 27x + 13 + -27x Combine like terms: -13x + -27x = -40x 13 + -40x + 14x2 = -13 + 27x + 13 + -27x Reorder the terms: 13 + -40x + 14x2 = -13 + 13 + 27x + -27x Combine like terms: -13 + 13 = 0 13 + -40x + 14x2 = 0 + 27x + -27x 13 + -40x + 14x2 = 27x + -27x Combine like terms: 27x + -27x = 0 13 + -40x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.9285714286 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '-0.9285714286' to each side of the equation. 0.9285714286 + -2.857142857x + -0.9285714286 + x2 = 0 + -0.9285714286 Reorder the terms: 0.9285714286 + -0.9285714286 + -2.857142857x + x2 = 0 + -0.9285714286 Combine like terms: 0.9285714286 + -0.9285714286 = 0.0000000000 0.0000000000 + -2.857142857x + x2 = 0 + -0.9285714286 -2.857142857x + x2 = 0 + -0.9285714286 Combine like terms: 0 + -0.9285714286 = -0.9285714286 -2.857142857x + x2 = -0.9285714286 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = -0.9285714286 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = -0.9285714286 + 2.040816328 Combine like terms: -0.9285714286 + 2.040816328 = 1.1122448994 2.040816328 + -2.857142857x + x2 = 1.1122448994 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 1.1122448994 Calculate the square root of the right side: 1.054630219 Break this problem into two subproblems by setting (x + -1.428571429) equal to 1.054630219 and -1.054630219.Subproblem 1
x + -1.428571429 = 1.054630219 Simplifying x + -1.428571429 = 1.054630219 Reorder the terms: -1.428571429 + x = 1.054630219 Solving -1.428571429 + x = 1.054630219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 1.054630219 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 1.054630219 + 1.428571429 x = 1.054630219 + 1.428571429 Combine like terms: 1.054630219 + 1.428571429 = 2.483201648 x = 2.483201648 Simplifying x = 2.483201648Subproblem 2
x + -1.428571429 = -1.054630219 Simplifying x + -1.428571429 = -1.054630219 Reorder the terms: -1.428571429 + x = -1.054630219 Solving -1.428571429 + x = -1.054630219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -1.054630219 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -1.054630219 + 1.428571429 x = -1.054630219 + 1.428571429 Combine like terms: -1.054630219 + 1.428571429 = 0.37394121 x = 0.37394121 Simplifying x = 0.37394121Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.483201648, 0.37394121}
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