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Simplifying 14x2 + 16x + -131 = 20 Reorder the terms: -131 + 16x + 14x2 = 20 Solving -131 + 16x + 14x2 = 20 Solving for variable 'x'. Reorder the terms: -131 + -20 + 16x + 14x2 = 20 + -20 Combine like terms: -131 + -20 = -151 -151 + 16x + 14x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -151 + 16x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -10.78571429 + 1.142857143x + x2 = 0 Move the constant term to the right: Add '10.78571429' to each side of the equation. -10.78571429 + 1.142857143x + 10.78571429 + x2 = 0 + 10.78571429 Reorder the terms: -10.78571429 + 10.78571429 + 1.142857143x + x2 = 0 + 10.78571429 Combine like terms: -10.78571429 + 10.78571429 = 0.00000000 0.00000000 + 1.142857143x + x2 = 0 + 10.78571429 1.142857143x + x2 = 0 + 10.78571429 Combine like terms: 0 + 10.78571429 = 10.78571429 1.142857143x + x2 = 10.78571429 The x term is 1.142857143x. Take half its coefficient (0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. 1.142857143x + 0.3265306123 + x2 = 10.78571429 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143x + x2 = 10.78571429 + 0.3265306123 Combine like terms: 10.78571429 + 0.3265306123 = 11.1122449023 0.3265306123 + 1.142857143x + x2 = 11.1122449023 Factor a perfect square on the left side: (x + 0.5714285715)(x + 0.5714285715) = 11.1122449023 Calculate the square root of the right side: 3.333503398 Break this problem into two subproblems by setting (x + 0.5714285715) equal to 3.333503398 and -3.333503398.Subproblem 1
x + 0.5714285715 = 3.333503398 Simplifying x + 0.5714285715 = 3.333503398 Reorder the terms: 0.5714285715 + x = 3.333503398 Solving 0.5714285715 + x = 3.333503398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + x = 3.333503398 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = 3.333503398 + -0.5714285715 x = 3.333503398 + -0.5714285715 Combine like terms: 3.333503398 + -0.5714285715 = 2.7620748265 x = 2.7620748265 Simplifying x = 2.7620748265Subproblem 2
x + 0.5714285715 = -3.333503398 Simplifying x + 0.5714285715 = -3.333503398 Reorder the terms: 0.5714285715 + x = -3.333503398 Solving 0.5714285715 + x = -3.333503398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + x = -3.333503398 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = -3.333503398 + -0.5714285715 x = -3.333503398 + -0.5714285715 Combine like terms: -3.333503398 + -0.5714285715 = -3.9049319695 x = -3.9049319695 Simplifying x = -3.9049319695Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7620748265, -3.9049319695}
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