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Simplifying 1.4x2 + -1x + -30 + -1x + -30 = 0 Reorder the terms: -30 + -30 + -1x + -1x + 1.4x2 = 0 Combine like terms: -30 + -30 = -60 -60 + -1x + -1x + 1.4x2 = 0 Combine like terms: -1x + -1x = -2x -60 + -2x + 1.4x2 = 0 Solving -60 + -2x + 1.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.4 the coefficient of the squared term: Divide each side by '1.4'. -42.85714286 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '42.85714286' to each side of the equation. -42.85714286 + -1.428571429x + 42.85714286 + x2 = 0 + 42.85714286 Reorder the terms: -42.85714286 + 42.85714286 + -1.428571429x + x2 = 0 + 42.85714286 Combine like terms: -42.85714286 + 42.85714286 = 0.00000000 0.00000000 + -1.428571429x + x2 = 0 + 42.85714286 -1.428571429x + x2 = 0 + 42.85714286 Combine like terms: 0 + 42.85714286 = 42.85714286 -1.428571429x + x2 = 42.85714286 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 = 42.85714286 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 42.85714286 + 0.5102040819 Combine like terms: 42.85714286 + 0.5102040819 = 43.3673469419 0.5102040819 + -1.428571429x + x2 = 43.3673469419 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 43.3673469419 Calculate the square root of the right side: 6.585388898 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 6.585388898 and -6.585388898.Subproblem 1
x + -0.7142857145 = 6.585388898 Simplifying x + -0.7142857145 = 6.585388898 Reorder the terms: -0.7142857145 + x = 6.585388898 Solving -0.7142857145 + x = 6.585388898 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 = 6.585388898 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 6.585388898 + 0.7142857145 x = 6.585388898 + 0.7142857145 Combine like terms: 6.585388898 + 0.7142857145 = 7.2996746125 x = 7.2996746125 Simplifying x = 7.2996746125Subproblem 2
x + -0.7142857145 = -6.585388898 Simplifying x + -0.7142857145 = -6.585388898 Reorder the terms: -0.7142857145 + x = -6.585388898 Solving -0.7142857145 + x = -6.585388898 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 = -6.585388898 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -6.585388898 + 0.7142857145 x = -6.585388898 + 0.7142857145 Combine like terms: -6.585388898 + 0.7142857145 = -5.8711031835 x = -5.8711031835 Simplifying x = -5.8711031835Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.2996746125, -5.8711031835}
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