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Simplifying 7x2 + 29x + -41 = 0 Reorder the terms: -41 + 29x + 7x2 = 0 Solving -41 + 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'. -5.857142857 + 4.142857143x + x2 = 0 Move the constant term to the right: Add '5.857142857' to each side of the equation. -5.857142857 + 4.142857143x + 5.857142857 + x2 = 0 + 5.857142857 Reorder the terms: -5.857142857 + 5.857142857 + 4.142857143x + x2 = 0 + 5.857142857 Combine like terms: -5.857142857 + 5.857142857 = 0.000000000 0.000000000 + 4.142857143x + x2 = 0 + 5.857142857 4.142857143x + x2 = 0 + 5.857142857 Combine like terms: 0 + 5.857142857 = 5.857142857 4.142857143x + x2 = 5.857142857 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 = 5.857142857 + 4.290816329 Reorder the terms: 4.290816329 + 4.142857143x + x2 = 5.857142857 + 4.290816329 Combine like terms: 5.857142857 + 4.290816329 = 10.147959186 4.290816329 + 4.142857143x + x2 = 10.147959186 Factor a perfect square on the left side: (x + 2.071428572)(x + 2.071428572) = 10.147959186 Calculate the square root of the right side: 3.185586161 Break this problem into two subproblems by setting (x + 2.071428572) equal to 3.185586161 and -3.185586161.Subproblem 1
x + 2.071428572 = 3.185586161 Simplifying x + 2.071428572 = 3.185586161 Reorder the terms: 2.071428572 + x = 3.185586161 Solving 2.071428572 + x = 3.185586161 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 = 3.185586161 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = 3.185586161 + -2.071428572 x = 3.185586161 + -2.071428572 Combine like terms: 3.185586161 + -2.071428572 = 1.114157589 x = 1.114157589 Simplifying x = 1.114157589Subproblem 2
x + 2.071428572 = -3.185586161 Simplifying x + 2.071428572 = -3.185586161 Reorder the terms: 2.071428572 + x = -3.185586161 Solving 2.071428572 + x = -3.185586161 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 = -3.185586161 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = -3.185586161 + -2.071428572 x = -3.185586161 + -2.071428572 Combine like terms: -3.185586161 + -2.071428572 = -5.257014733 x = -5.257014733 Simplifying x = -5.257014733Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.114157589, -5.257014733}
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