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Simplifying 15x2 + 31x + -10 = 0 Reorder the terms: -10 + 31x + 15x2 = 0 Solving -10 + 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'. -0.6666666667 + 2.066666667x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 2.066666667x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 2.066666667x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 2.066666667x + x2 = 0 + 0.6666666667 2.066666667x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 2.066666667x + x2 = 0.6666666667 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 = 0.6666666667 + 1.067777779 Reorder the terms: 1.067777779 + 2.066666667x + x2 = 0.6666666667 + 1.067777779 Combine like terms: 0.6666666667 + 1.067777779 = 1.7344444457 1.067777779 + 2.066666667x + x2 = 1.7344444457 Factor a perfect square on the left side: (x + 1.033333334)(x + 1.033333334) = 1.7344444457 Calculate the square root of the right side: 1.316983085 Break this problem into two subproblems by setting (x + 1.033333334) equal to 1.316983085 and -1.316983085.Subproblem 1
x + 1.033333334 = 1.316983085 Simplifying x + 1.033333334 = 1.316983085 Reorder the terms: 1.033333334 + x = 1.316983085 Solving 1.033333334 + x = 1.316983085 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 = 1.316983085 + -1.033333334 Combine like terms: 1.033333334 + -1.033333334 = 0.000000000 0.000000000 + x = 1.316983085 + -1.033333334 x = 1.316983085 + -1.033333334 Combine like terms: 1.316983085 + -1.033333334 = 0.283649751 x = 0.283649751 Simplifying x = 0.283649751Subproblem 2
x + 1.033333334 = -1.316983085 Simplifying x + 1.033333334 = -1.316983085 Reorder the terms: 1.033333334 + x = -1.316983085 Solving 1.033333334 + x = -1.316983085 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 = -1.316983085 + -1.033333334 Combine like terms: 1.033333334 + -1.033333334 = 0.000000000 0.000000000 + x = -1.316983085 + -1.033333334 x = -1.316983085 + -1.033333334 Combine like terms: -1.316983085 + -1.033333334 = -2.350316419 x = -2.350316419 Simplifying x = -2.350316419Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.283649751, -2.350316419}
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