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Simplifying 3.5x2 + 5x + -2.5 = 0 Reorder the terms: -2.5 + 5x + 3.5x2 = 0 Solving -2.5 + 5x + 3.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. -0.7142857143 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 1.428571429x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 1.428571429x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 1.428571429x + x2 = 0 + 0.7142857143 1.428571429x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 1.428571429x + x2 = 0.7142857143 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 = 0.7142857143 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 0.7142857143 + 0.5102040819 Combine like terms: 0.7142857143 + 0.5102040819 = 1.2244897962 0.5102040819 + 1.428571429x + x2 = 1.2244897962 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 1.2244897962 Calculate the square root of the right side: 1.10656667 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 1.10656667 and -1.10656667.Subproblem 1
x + 0.7142857145 = 1.10656667 Simplifying x + 0.7142857145 = 1.10656667 Reorder the terms: 0.7142857145 + x = 1.10656667 Solving 0.7142857145 + x = 1.10656667 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 = 1.10656667 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 1.10656667 + -0.7142857145 x = 1.10656667 + -0.7142857145 Combine like terms: 1.10656667 + -0.7142857145 = 0.3922809555 x = 0.3922809555 Simplifying x = 0.3922809555Subproblem 2
x + 0.7142857145 = -1.10656667 Simplifying x + 0.7142857145 = -1.10656667 Reorder the terms: 0.7142857145 + x = -1.10656667 Solving 0.7142857145 + x = -1.10656667 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 = -1.10656667 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -1.10656667 + -0.7142857145 x = -1.10656667 + -0.7142857145 Combine like terms: -1.10656667 + -0.7142857145 = -1.8208523845 x = -1.8208523845 Simplifying x = -1.8208523845Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3922809555, -1.8208523845}
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