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Simplifying 14x2 + -16x + -15 = 0 Reorder the terms: -15 + -16x + 14x2 = 0 Solving -15 + -16x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.071428571 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '1.071428571' to each side of the equation. -1.071428571 + -1.142857143x + 1.071428571 + x2 = 0 + 1.071428571 Reorder the terms: -1.071428571 + 1.071428571 + -1.142857143x + x2 = 0 + 1.071428571 Combine like terms: -1.071428571 + 1.071428571 = 0.000000000 0.000000000 + -1.142857143x + x2 = 0 + 1.071428571 -1.142857143x + x2 = 0 + 1.071428571 Combine like terms: 0 + 1.071428571 = 1.071428571 -1.142857143x + x2 = 1.071428571 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 = 1.071428571 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 1.071428571 + 0.3265306123 Combine like terms: 1.071428571 + 0.3265306123 = 1.3979591833 0.3265306123 + -1.142857143x + x2 = 1.3979591833 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 1.3979591833 Calculate the square root of the right side: 1.18235324 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 1.18235324 and -1.18235324.Subproblem 1
x + -0.5714285715 = 1.18235324 Simplifying x + -0.5714285715 = 1.18235324 Reorder the terms: -0.5714285715 + x = 1.18235324 Solving -0.5714285715 + x = 1.18235324 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 = 1.18235324 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 1.18235324 + 0.5714285715 x = 1.18235324 + 0.5714285715 Combine like terms: 1.18235324 + 0.5714285715 = 1.7537818115 x = 1.7537818115 Simplifying x = 1.7537818115Subproblem 2
x + -0.5714285715 = -1.18235324 Simplifying x + -0.5714285715 = -1.18235324 Reorder the terms: -0.5714285715 + x = -1.18235324 Solving -0.5714285715 + x = -1.18235324 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 = -1.18235324 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -1.18235324 + 0.5714285715 x = -1.18235324 + 0.5714285715 Combine like terms: -1.18235324 + 0.5714285715 = -0.6109246685 x = -0.6109246685 Simplifying x = -0.6109246685Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7537818115, -0.6109246685}
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