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Simplifying 11x2 + 40x + -500 = 0 Reorder the terms: -500 + 40x + 11x2 = 0 Solving -500 + 40x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -45.45454545 + 3.636363636x + x2 = 0 Move the constant term to the right: Add '45.45454545' to each side of the equation. -45.45454545 + 3.636363636x + 45.45454545 + x2 = 0 + 45.45454545 Reorder the terms: -45.45454545 + 45.45454545 + 3.636363636x + x2 = 0 + 45.45454545 Combine like terms: -45.45454545 + 45.45454545 = 0.00000000 0.00000000 + 3.636363636x + x2 = 0 + 45.45454545 3.636363636x + x2 = 0 + 45.45454545 Combine like terms: 0 + 45.45454545 = 45.45454545 3.636363636x + x2 = 45.45454545 The x term is 3.636363636x. Take half its coefficient (1.818181818). Square it (3.305785123) and add it to both sides. Add '3.305785123' to each side of the equation. 3.636363636x + 3.305785123 + x2 = 45.45454545 + 3.305785123 Reorder the terms: 3.305785123 + 3.636363636x + x2 = 45.45454545 + 3.305785123 Combine like terms: 45.45454545 + 3.305785123 = 48.760330573 3.305785123 + 3.636363636x + x2 = 48.760330573 Factor a perfect square on the left side: (x + 1.818181818)(x + 1.818181818) = 48.760330573 Calculate the square root of the right side: 6.98285977 Break this problem into two subproblems by setting (x + 1.818181818) equal to 6.98285977 and -6.98285977.Subproblem 1
x + 1.818181818 = 6.98285977 Simplifying x + 1.818181818 = 6.98285977 Reorder the terms: 1.818181818 + x = 6.98285977 Solving 1.818181818 + x = 6.98285977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.818181818' to each side of the equation. 1.818181818 + -1.818181818 + x = 6.98285977 + -1.818181818 Combine like terms: 1.818181818 + -1.818181818 = 0.000000000 0.000000000 + x = 6.98285977 + -1.818181818 x = 6.98285977 + -1.818181818 Combine like terms: 6.98285977 + -1.818181818 = 5.164677952 x = 5.164677952 Simplifying x = 5.164677952Subproblem 2
x + 1.818181818 = -6.98285977 Simplifying x + 1.818181818 = -6.98285977 Reorder the terms: 1.818181818 + x = -6.98285977 Solving 1.818181818 + x = -6.98285977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.818181818' to each side of the equation. 1.818181818 + -1.818181818 + x = -6.98285977 + -1.818181818 Combine like terms: 1.818181818 + -1.818181818 = 0.000000000 0.000000000 + x = -6.98285977 + -1.818181818 x = -6.98285977 + -1.818181818 Combine like terms: -6.98285977 + -1.818181818 = -8.801041588 x = -8.801041588 Simplifying x = -8.801041588Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.164677952, -8.801041588}
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