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Simplifying 35x2 + 50x + -74 = 0 Reorder the terms: -74 + 50x + 35x2 = 0 Solving -74 + 50x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -2.114285714 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '2.114285714' to each side of the equation. -2.114285714 + 1.428571429x + 2.114285714 + x2 = 0 + 2.114285714 Reorder the terms: -2.114285714 + 2.114285714 + 1.428571429x + x2 = 0 + 2.114285714 Combine like terms: -2.114285714 + 2.114285714 = 0.000000000 0.000000000 + 1.428571429x + x2 = 0 + 2.114285714 1.428571429x + x2 = 0 + 2.114285714 Combine like terms: 0 + 2.114285714 = 2.114285714 1.428571429x + x2 = 2.114285714 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 = 2.114285714 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 2.114285714 + 0.5102040819 Combine like terms: 2.114285714 + 0.5102040819 = 2.6244897959 0.5102040819 + 1.428571429x + x2 = 2.6244897959 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 2.6244897959 Calculate the square root of the right side: 1.620027715 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 1.620027715 and -1.620027715.Subproblem 1
x + 0.7142857145 = 1.620027715 Simplifying x + 0.7142857145 = 1.620027715 Reorder the terms: 0.7142857145 + x = 1.620027715 Solving 0.7142857145 + x = 1.620027715 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 = 1.620027715 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 1.620027715 + -0.7142857145 x = 1.620027715 + -0.7142857145 Combine like terms: 1.620027715 + -0.7142857145 = 0.9057420005 x = 0.9057420005 Simplifying x = 0.9057420005Subproblem 2
x + 0.7142857145 = -1.620027715 Simplifying x + 0.7142857145 = -1.620027715 Reorder the terms: 0.7142857145 + x = -1.620027715 Solving 0.7142857145 + x = -1.620027715 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 = -1.620027715 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -1.620027715 + -0.7142857145 x = -1.620027715 + -0.7142857145 Combine like terms: -1.620027715 + -0.7142857145 = -2.3343134295 x = -2.3343134295 Simplifying x = -2.3343134295Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9057420005, -2.3343134295}
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