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Simplifying 7x2 + 45x + -41 = 0 Reorder the terms: -41 + 45x + 7x2 = 0 Solving -41 + 45x + 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 + 6.428571429x + x2 = 0 Move the constant term to the right: Add '5.857142857' to each side of the equation. -5.857142857 + 6.428571429x + 5.857142857 + x2 = 0 + 5.857142857 Reorder the terms: -5.857142857 + 5.857142857 + 6.428571429x + x2 = 0 + 5.857142857 Combine like terms: -5.857142857 + 5.857142857 = 0.000000000 0.000000000 + 6.428571429x + x2 = 0 + 5.857142857 6.428571429x + x2 = 0 + 5.857142857 Combine like terms: 0 + 5.857142857 = 5.857142857 6.428571429x + x2 = 5.857142857 The x term is 6.428571429x. Take half its coefficient (3.214285715). Square it (10.33163266) and add it to both sides. Add '10.33163266' to each side of the equation. 6.428571429x + 10.33163266 + x2 = 5.857142857 + 10.33163266 Reorder the terms: 10.33163266 + 6.428571429x + x2 = 5.857142857 + 10.33163266 Combine like terms: 5.857142857 + 10.33163266 = 16.188775517 10.33163266 + 6.428571429x + x2 = 16.188775517 Factor a perfect square on the left side: (x + 3.214285715)(x + 3.214285715) = 16.188775517 Calculate the square root of the right side: 4.023527745 Break this problem into two subproblems by setting (x + 3.214285715) equal to 4.023527745 and -4.023527745.Subproblem 1
x + 3.214285715 = 4.023527745 Simplifying x + 3.214285715 = 4.023527745 Reorder the terms: 3.214285715 + x = 4.023527745 Solving 3.214285715 + x = 4.023527745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.214285715' to each side of the equation. 3.214285715 + -3.214285715 + x = 4.023527745 + -3.214285715 Combine like terms: 3.214285715 + -3.214285715 = 0.000000000 0.000000000 + x = 4.023527745 + -3.214285715 x = 4.023527745 + -3.214285715 Combine like terms: 4.023527745 + -3.214285715 = 0.80924203 x = 0.80924203 Simplifying x = 0.80924203Subproblem 2
x + 3.214285715 = -4.023527745 Simplifying x + 3.214285715 = -4.023527745 Reorder the terms: 3.214285715 + x = -4.023527745 Solving 3.214285715 + x = -4.023527745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.214285715' to each side of the equation. 3.214285715 + -3.214285715 + x = -4.023527745 + -3.214285715 Combine like terms: 3.214285715 + -3.214285715 = 0.000000000 0.000000000 + x = -4.023527745 + -3.214285715 x = -4.023527745 + -3.214285715 Combine like terms: -4.023527745 + -3.214285715 = -7.23781346 x = -7.23781346 Simplifying x = -7.23781346Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.80924203, -7.23781346}
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