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Simplifying 49x2 + 70x + 25 = 10 Reorder the terms: 25 + 70x + 49x2 = 10 Solving 25 + 70x + 49x2 = 10 Solving for variable 'x'. Reorder the terms: 25 + -10 + 70x + 49x2 = 10 + -10 Combine like terms: 25 + -10 = 15 15 + 70x + 49x2 = 10 + -10 Combine like terms: 10 + -10 = 0 15 + 70x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.306122449 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '-0.306122449' to each side of the equation. 0.306122449 + 1.428571429x + -0.306122449 + x2 = 0 + -0.306122449 Reorder the terms: 0.306122449 + -0.306122449 + 1.428571429x + x2 = 0 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + 1.428571429x + x2 = 0 + -0.306122449 1.428571429x + x2 = 0 + -0.306122449 Combine like terms: 0 + -0.306122449 = -0.306122449 1.428571429x + x2 = -0.306122449 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 = -0.306122449 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = -0.306122449 + 0.5102040819 Combine like terms: -0.306122449 + 0.5102040819 = 0.2040816329 0.5102040819 + 1.428571429x + x2 = 0.2040816329 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 0.2040816329 Calculate the square root of the right side: 0.451753952 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 0.451753952 and -0.451753952.Subproblem 1
x + 0.7142857145 = 0.451753952 Simplifying x + 0.7142857145 = 0.451753952 Reorder the terms: 0.7142857145 + x = 0.451753952 Solving 0.7142857145 + x = 0.451753952 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 = 0.451753952 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 0.451753952 + -0.7142857145 x = 0.451753952 + -0.7142857145 Combine like terms: 0.451753952 + -0.7142857145 = -0.2625317625 x = -0.2625317625 Simplifying x = -0.2625317625Subproblem 2
x + 0.7142857145 = -0.451753952 Simplifying x + 0.7142857145 = -0.451753952 Reorder the terms: 0.7142857145 + x = -0.451753952 Solving 0.7142857145 + x = -0.451753952 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 = -0.451753952 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -0.451753952 + -0.7142857145 x = -0.451753952 + -0.7142857145 Combine like terms: -0.451753952 + -0.7142857145 = -1.1660396665 x = -1.1660396665 Simplifying x = -1.1660396665Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2625317625, -1.1660396665}
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