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Simplifying 7x2 + -29x + 18 = 0 Reorder the terms: 18 + -29x + 7x2 = 0 Solving 18 + -29x + 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'. 2.571428571 + -4.142857143x + x2 = 0 Move the constant term to the right: Add '-2.571428571' to each side of the equation. 2.571428571 + -4.142857143x + -2.571428571 + x2 = 0 + -2.571428571 Reorder the terms: 2.571428571 + -2.571428571 + -4.142857143x + x2 = 0 + -2.571428571 Combine like terms: 2.571428571 + -2.571428571 = 0.000000000 0.000000000 + -4.142857143x + x2 = 0 + -2.571428571 -4.142857143x + x2 = 0 + -2.571428571 Combine like terms: 0 + -2.571428571 = -2.571428571 -4.142857143x + x2 = -2.571428571 The x term is -4.142857143x. Take half its coefficient (-2.071428572). Square it (4.290816329) and add it to both sides. Add '4.290816329' to each side of the equation. -4.142857143x + 4.290816329 + x2 = -2.571428571 + 4.290816329 Reorder the terms: 4.290816329 + -4.142857143x + x2 = -2.571428571 + 4.290816329 Combine like terms: -2.571428571 + 4.290816329 = 1.719387758 4.290816329 + -4.142857143x + x2 = 1.719387758 Factor a perfect square on the left side: (x + -2.071428572)(x + -2.071428572) = 1.719387758 Calculate the square root of the right side: 1.311254269 Break this problem into two subproblems by setting (x + -2.071428572) equal to 1.311254269 and -1.311254269.Subproblem 1
x + -2.071428572 = 1.311254269 Simplifying x + -2.071428572 = 1.311254269 Reorder the terms: -2.071428572 + x = 1.311254269 Solving -2.071428572 + x = 1.311254269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + x = 1.311254269 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = 1.311254269 + 2.071428572 x = 1.311254269 + 2.071428572 Combine like terms: 1.311254269 + 2.071428572 = 3.382682841 x = 3.382682841 Simplifying x = 3.382682841Subproblem 2
x + -2.071428572 = -1.311254269 Simplifying x + -2.071428572 = -1.311254269 Reorder the terms: -2.071428572 + x = -1.311254269 Solving -2.071428572 + x = -1.311254269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + x = -1.311254269 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = -1.311254269 + 2.071428572 x = -1.311254269 + 2.071428572 Combine like terms: -1.311254269 + 2.071428572 = 0.760174303 x = 0.760174303 Simplifying x = 0.760174303Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.382682841, 0.760174303}
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