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Simplifying 15x2 + -31x + 15 = 0 Reorder the terms: 15 + -31x + 15x2 = 0 Solving 15 + -31x + 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'. 1 + -2.066666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.066666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.066666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.066666667x + x2 = 0 + -1 -2.066666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.066666667x + x2 = -1 The x term is -2.066666667x. Take half its coefficient (-1.033333334). Square it (1.067777779) and add it to both sides. Add '1.067777779' to each side of the equation. -2.066666667x + 1.067777779 + x2 = -1 + 1.067777779 Reorder the terms: 1.067777779 + -2.066666667x + x2 = -1 + 1.067777779 Combine like terms: -1 + 1.067777779 = 0.067777779 1.067777779 + -2.066666667x + x2 = 0.067777779 Factor a perfect square on the left side: (x + -1.033333334)(x + -1.033333334) = 0.067777779 Calculate the square root of the right side: 0.260341658 Break this problem into two subproblems by setting (x + -1.033333334) equal to 0.260341658 and -0.260341658.Subproblem 1
x + -1.033333334 = 0.260341658 Simplifying x + -1.033333334 = 0.260341658 Reorder the terms: -1.033333334 + x = 0.260341658 Solving -1.033333334 + x = 0.260341658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.033333334' to each side of the equation. -1.033333334 + 1.033333334 + x = 0.260341658 + 1.033333334 Combine like terms: -1.033333334 + 1.033333334 = 0.000000000 0.000000000 + x = 0.260341658 + 1.033333334 x = 0.260341658 + 1.033333334 Combine like terms: 0.260341658 + 1.033333334 = 1.293674992 x = 1.293674992 Simplifying x = 1.293674992Subproblem 2
x + -1.033333334 = -0.260341658 Simplifying x + -1.033333334 = -0.260341658 Reorder the terms: -1.033333334 + x = -0.260341658 Solving -1.033333334 + x = -0.260341658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.033333334' to each side of the equation. -1.033333334 + 1.033333334 + x = -0.260341658 + 1.033333334 Combine like terms: -1.033333334 + 1.033333334 = 0.000000000 0.000000000 + x = -0.260341658 + 1.033333334 x = -0.260341658 + 1.033333334 Combine like terms: -0.260341658 + 1.033333334 = 0.772991676 x = 0.772991676 Simplifying x = 0.772991676Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.293674992, 0.772991676}
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