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Simplifying 200 = (0.05x2) + 2.2x + 0.16 Reorder the terms: 200 = 0.16 + 2.2x + (0.05x2) Solving 200 = 0.16 + 2.2x + (0.05x2) Solving for variable 'x'. Combine like terms: 200 + -0.16 = 199.84 199.84 + -2.2x + (-0.05x2) = 0.16 + 2.2x + (0.05x2) + -0.16 + -2.2x + (-0.05x2) Reorder the terms: 199.84 + -2.2x + (-0.05x2) = 0.16 + -0.16 + 2.2x + -2.2x + (0.05x2) + (-0.05x2) Combine like terms: 0.16 + -0.16 = 0.00 199.84 + -2.2x + (-0.05x2) = 0.00 + 2.2x + -2.2x + (0.05x2) + (-0.05x2) 199.84 + -2.2x + (-0.05x2) = 2.2x + -2.2x + (0.05x2) + (-0.05x2) Combine like terms: 2.2x + -2.2x = 0.0 199.84 + -2.2x + (-0.05x2) = 0.0 + (0.05x2) + (-0.05x2) 199.84 + -2.2x + (-0.05x2) = (0.05x2) + (-0.05x2) Combine like terms: (0.05x2) + (-0.05x2) = 0.00 199.84 + -2.2x + (-0.05x2) = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -3996.8 + 44x + x2 = 0 Move the constant term to the right: Add '3996.8' to each side of the equation. -3996.8 + 44x + 3996.8 + x2 = 0 + 3996.8 Reorder the terms: -3996.8 + 3996.8 + 44x + x2 = 0 + 3996.8 Combine like terms: -3996.8 + 3996.8 = 0.0 0.0 + 44x + x2 = 0 + 3996.8 44x + x2 = 0 + 3996.8 Combine like terms: 0 + 3996.8 = 3996.8 44x + x2 = 3996.8 The x term is 44x. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44x + 484 + x2 = 3996.8 + 484 Reorder the terms: 484 + 44x + x2 = 3996.8 + 484 Combine like terms: 3996.8 + 484 = 4480.8 484 + 44x + x2 = 4480.8 Factor a perfect square on the left side: ((x) + 22)((x) + 22) = 4480.8 Calculate the square root of the right side: 66.938777999 Break this problem into two subproblems by setting ((x) + 22) equal to 66.938777999 and -66.938777999.Subproblem 1
(x) + 22 = 66.938777999 Simplifying (x) + 22 = 66.938777999 x + 22 = 66.938777999 Reorder the terms: 22 + x = 66.938777999 Solving 22 + x = 66.938777999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 66.938777999 + -22 Combine like terms: 22 + -22 = 0 0 + x = 66.938777999 + -22 x = 66.938777999 + -22 Combine like terms: 66.938777999 + -22 = 44.938777999 x = 44.938777999 Simplifying x = 44.938777999Subproblem 2
(x) + 22 = -66.938777999 Simplifying (x) + 22 = -66.938777999 x + 22 = -66.938777999 Reorder the terms: 22 + x = -66.938777999 Solving 22 + x = -66.938777999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = -66.938777999 + -22 Combine like terms: 22 + -22 = 0 0 + x = -66.938777999 + -22 x = -66.938777999 + -22 Combine like terms: -66.938777999 + -22 = -88.938777999 x = -88.938777999 Simplifying x = -88.938777999Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.938777999, -88.938777999}
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