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Simplifying 43x + -15x2 + -11 = 0 Reorder the terms: -11 + 43x + -15x2 = 0 Solving -11 + 43x + -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'. 0.7333333333 + -2.866666667x + x2 = 0 Move the constant term to the right: Add '-0.7333333333' to each side of the equation. 0.7333333333 + -2.866666667x + -0.7333333333 + x2 = 0 + -0.7333333333 Reorder the terms: 0.7333333333 + -0.7333333333 + -2.866666667x + x2 = 0 + -0.7333333333 Combine like terms: 0.7333333333 + -0.7333333333 = 0.0000000000 0.0000000000 + -2.866666667x + x2 = 0 + -0.7333333333 -2.866666667x + x2 = 0 + -0.7333333333 Combine like terms: 0 + -0.7333333333 = -0.7333333333 -2.866666667x + x2 = -0.7333333333 The x term is -2.866666667x. Take half its coefficient (-1.433333334). Square it (2.054444446) and add it to both sides. Add '2.054444446' to each side of the equation. -2.866666667x + 2.054444446 + x2 = -0.7333333333 + 2.054444446 Reorder the terms: 2.054444446 + -2.866666667x + x2 = -0.7333333333 + 2.054444446 Combine like terms: -0.7333333333 + 2.054444446 = 1.3211111127 2.054444446 + -2.866666667x + x2 = 1.3211111127 Factor a perfect square on the left side: (x + -1.433333334)(x + -1.433333334) = 1.3211111127 Calculate the square root of the right side: 1.149395977 Break this problem into two subproblems by setting (x + -1.433333334) equal to 1.149395977 and -1.149395977.Subproblem 1
x + -1.433333334 = 1.149395977 Simplifying x + -1.433333334 = 1.149395977 Reorder the terms: -1.433333334 + x = 1.149395977 Solving -1.433333334 + x = 1.149395977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.433333334' to each side of the equation. -1.433333334 + 1.433333334 + x = 1.149395977 + 1.433333334 Combine like terms: -1.433333334 + 1.433333334 = 0.000000000 0.000000000 + x = 1.149395977 + 1.433333334 x = 1.149395977 + 1.433333334 Combine like terms: 1.149395977 + 1.433333334 = 2.582729311 x = 2.582729311 Simplifying x = 2.582729311Subproblem 2
x + -1.433333334 = -1.149395977 Simplifying x + -1.433333334 = -1.149395977 Reorder the terms: -1.433333334 + x = -1.149395977 Solving -1.433333334 + x = -1.149395977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.433333334' to each side of the equation. -1.433333334 + 1.433333334 + x = -1.149395977 + 1.433333334 Combine like terms: -1.433333334 + 1.433333334 = 0.000000000 0.000000000 + x = -1.149395977 + 1.433333334 x = -1.149395977 + 1.433333334 Combine like terms: -1.149395977 + 1.433333334 = 0.283937357 x = 0.283937357 Simplifying x = 0.283937357Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.582729311, 0.283937357}
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