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Simplifying 14x2 + -111x + 8 = 0 Reorder the terms: 8 + -111x + 14x2 = 0 Solving 8 + -111x + 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'. 0.5714285714 + -7.928571429x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -7.928571429x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -7.928571429x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -7.928571429x + x2 = 0 + -0.5714285714 -7.928571429x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -7.928571429x + x2 = -0.5714285714 The x term is -7.928571429x. Take half its coefficient (-3.964285715). Square it (15.71556123) and add it to both sides. Add '15.71556123' to each side of the equation. -7.928571429x + 15.71556123 + x2 = -0.5714285714 + 15.71556123 Reorder the terms: 15.71556123 + -7.928571429x + x2 = -0.5714285714 + 15.71556123 Combine like terms: -0.5714285714 + 15.71556123 = 15.1441326586 15.71556123 + -7.928571429x + x2 = 15.1441326586 Factor a perfect square on the left side: (x + -3.964285715)(x + -3.964285715) = 15.1441326586 Calculate the square root of the right side: 3.891546307 Break this problem into two subproblems by setting (x + -3.964285715) equal to 3.891546307 and -3.891546307.Subproblem 1
x + -3.964285715 = 3.891546307 Simplifying x + -3.964285715 = 3.891546307 Reorder the terms: -3.964285715 + x = 3.891546307 Solving -3.964285715 + x = 3.891546307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.964285715' to each side of the equation. -3.964285715 + 3.964285715 + x = 3.891546307 + 3.964285715 Combine like terms: -3.964285715 + 3.964285715 = 0.000000000 0.000000000 + x = 3.891546307 + 3.964285715 x = 3.891546307 + 3.964285715 Combine like terms: 3.891546307 + 3.964285715 = 7.855832022 x = 7.855832022 Simplifying x = 7.855832022Subproblem 2
x + -3.964285715 = -3.891546307 Simplifying x + -3.964285715 = -3.891546307 Reorder the terms: -3.964285715 + x = -3.891546307 Solving -3.964285715 + x = -3.891546307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.964285715' to each side of the equation. -3.964285715 + 3.964285715 + x = -3.891546307 + 3.964285715 Combine like terms: -3.964285715 + 3.964285715 = 0.000000000 0.000000000 + x = -3.891546307 + 3.964285715 x = -3.891546307 + 3.964285715 Combine like terms: -3.891546307 + 3.964285715 = 0.072739408 x = 0.072739408 Simplifying x = 0.072739408Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.855832022, 0.072739408}
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