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Simplifying 14x2 + 55x + -167 = 0 Reorder the terms: -167 + 55x + 14x2 = 0 Solving -167 + 55x + 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'. -11.92857143 + 3.928571429x + x2 = 0 Move the constant term to the right: Add '11.92857143' to each side of the equation. -11.92857143 + 3.928571429x + 11.92857143 + x2 = 0 + 11.92857143 Reorder the terms: -11.92857143 + 11.92857143 + 3.928571429x + x2 = 0 + 11.92857143 Combine like terms: -11.92857143 + 11.92857143 = 0.00000000 0.00000000 + 3.928571429x + x2 = 0 + 11.92857143 3.928571429x + x2 = 0 + 11.92857143 Combine like terms: 0 + 11.92857143 = 11.92857143 3.928571429x + x2 = 11.92857143 The x term is 3.928571429x. Take half its coefficient (1.964285715). Square it (3.858418370) and add it to both sides. Add '3.858418370' to each side of the equation. 3.928571429x + 3.858418370 + x2 = 11.92857143 + 3.858418370 Reorder the terms: 3.858418370 + 3.928571429x + x2 = 11.92857143 + 3.858418370 Combine like terms: 11.92857143 + 3.858418370 = 15.7869898 3.858418370 + 3.928571429x + x2 = 15.7869898 Factor a perfect square on the left side: (x + 1.964285715)(x + 1.964285715) = 15.7869898 Calculate the square root of the right side: 3.97328451 Break this problem into two subproblems by setting (x + 1.964285715) equal to 3.97328451 and -3.97328451.Subproblem 1
x + 1.964285715 = 3.97328451 Simplifying x + 1.964285715 = 3.97328451 Reorder the terms: 1.964285715 + x = 3.97328451 Solving 1.964285715 + x = 3.97328451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.964285715' to each side of the equation. 1.964285715 + -1.964285715 + x = 3.97328451 + -1.964285715 Combine like terms: 1.964285715 + -1.964285715 = 0.000000000 0.000000000 + x = 3.97328451 + -1.964285715 x = 3.97328451 + -1.964285715 Combine like terms: 3.97328451 + -1.964285715 = 2.008998795 x = 2.008998795 Simplifying x = 2.008998795Subproblem 2
x + 1.964285715 = -3.97328451 Simplifying x + 1.964285715 = -3.97328451 Reorder the terms: 1.964285715 + x = -3.97328451 Solving 1.964285715 + x = -3.97328451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.964285715' to each side of the equation. 1.964285715 + -1.964285715 + x = -3.97328451 + -1.964285715 Combine like terms: 1.964285715 + -1.964285715 = 0.000000000 0.000000000 + x = -3.97328451 + -1.964285715 x = -3.97328451 + -1.964285715 Combine like terms: -3.97328451 + -1.964285715 = -5.937570225 x = -5.937570225 Simplifying x = -5.937570225Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.008998795, -5.937570225}
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