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Simplifying 7x2 + -10x + -111 = 0 Reorder the terms: -111 + -10x + 7x2 = 0 Solving -111 + -10x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -15.85714286 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '15.85714286' to each side of the equation. -15.85714286 + -1.428571429x + 15.85714286 + x2 = 0 + 15.85714286 Reorder the terms: -15.85714286 + 15.85714286 + -1.428571429x + x2 = 0 + 15.85714286 Combine like terms: -15.85714286 + 15.85714286 = 0.00000000 0.00000000 + -1.428571429x + x2 = 0 + 15.85714286 -1.428571429x + x2 = 0 + 15.85714286 Combine like terms: 0 + 15.85714286 = 15.85714286 -1.428571429x + x2 = 15.85714286 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 15.85714286 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 15.85714286 + 0.5102040819 Combine like terms: 15.85714286 + 0.5102040819 = 16.3673469419 0.5102040819 + -1.428571429x + x2 = 16.3673469419 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 16.3673469419 Calculate the square root of the right side: 4.045657789 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 4.045657789 and -4.045657789.Subproblem 1
x + -0.7142857145 = 4.045657789 Simplifying x + -0.7142857145 = 4.045657789 Reorder the terms: -0.7142857145 + x = 4.045657789 Solving -0.7142857145 + x = 4.045657789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 4.045657789 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 4.045657789 + 0.7142857145 x = 4.045657789 + 0.7142857145 Combine like terms: 4.045657789 + 0.7142857145 = 4.7599435035 x = 4.7599435035 Simplifying x = 4.7599435035Subproblem 2
x + -0.7142857145 = -4.045657789 Simplifying x + -0.7142857145 = -4.045657789 Reorder the terms: -0.7142857145 + x = -4.045657789 Solving -0.7142857145 + x = -4.045657789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -4.045657789 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -4.045657789 + 0.7142857145 x = -4.045657789 + 0.7142857145 Combine like terms: -4.045657789 + 0.7142857145 = -3.3313720745 x = -3.3313720745 Simplifying x = -3.3313720745Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.7599435035, -3.3313720745}
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