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Simplifying X = -3.6X2 + -8.8X + 8.3 Reorder the terms: X = 8.3 + -8.8X + -3.6X2 Solving X = 8.3 + -8.8X + -3.6X2 Solving for variable 'X'. Reorder the terms: -8.3 + X + 8.8X + 3.6X2 = 8.3 + -8.8X + -3.6X2 + -8.3 + 8.8X + 3.6X2 Combine like terms: X + 8.8X = 9.8X -8.3 + 9.8X + 3.6X2 = 8.3 + -8.8X + -3.6X2 + -8.3 + 8.8X + 3.6X2 Reorder the terms: -8.3 + 9.8X + 3.6X2 = 8.3 + -8.3 + -8.8X + 8.8X + -3.6X2 + 3.6X2 Combine like terms: 8.3 + -8.3 = 0.0 -8.3 + 9.8X + 3.6X2 = 0.0 + -8.8X + 8.8X + -3.6X2 + 3.6X2 -8.3 + 9.8X + 3.6X2 = -8.8X + 8.8X + -3.6X2 + 3.6X2 Combine like terms: -8.8X + 8.8X = 0.0 -8.3 + 9.8X + 3.6X2 = 0.0 + -3.6X2 + 3.6X2 -8.3 + 9.8X + 3.6X2 = -3.6X2 + 3.6X2 Combine like terms: -3.6X2 + 3.6X2 = 0.0 -8.3 + 9.8X + 3.6X2 = 0.0 Begin completing the square. Divide all terms by 3.6 the coefficient of the squared term: Divide each side by '3.6'. -2.305555556 + 2.722222222X + X2 = 0 Move the constant term to the right: Add '2.305555556' to each side of the equation. -2.305555556 + 2.722222222X + 2.305555556 + X2 = 0 + 2.305555556 Reorder the terms: -2.305555556 + 2.305555556 + 2.722222222X + X2 = 0 + 2.305555556 Combine like terms: -2.305555556 + 2.305555556 = 0.000000000 0.000000000 + 2.722222222X + X2 = 0 + 2.305555556 2.722222222X + X2 = 0 + 2.305555556 Combine like terms: 0 + 2.305555556 = 2.305555556 2.722222222X + X2 = 2.305555556 The X term is 2.722222222X. Take half its coefficient (1.361111111). Square it (1.852623456) and add it to both sides. Add '1.852623456' to each side of the equation. 2.722222222X + 1.852623456 + X2 = 2.305555556 + 1.852623456 Reorder the terms: 1.852623456 + 2.722222222X + X2 = 2.305555556 + 1.852623456 Combine like terms: 2.305555556 + 1.852623456 = 4.158179012 1.852623456 + 2.722222222X + X2 = 4.158179012 Factor a perfect square on the left side: (X + 1.361111111)(X + 1.361111111) = 4.158179012 Calculate the square root of the right side: 2.03916135 Break this problem into two subproblems by setting (X + 1.361111111) equal to 2.03916135 and -2.03916135.Subproblem 1
X + 1.361111111 = 2.03916135 Simplifying X + 1.361111111 = 2.03916135 Reorder the terms: 1.361111111 + X = 2.03916135 Solving 1.361111111 + X = 2.03916135 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.361111111' to each side of the equation. 1.361111111 + -1.361111111 + X = 2.03916135 + -1.361111111 Combine like terms: 1.361111111 + -1.361111111 = 0.000000000 0.000000000 + X = 2.03916135 + -1.361111111 X = 2.03916135 + -1.361111111 Combine like terms: 2.03916135 + -1.361111111 = 0.678050239 X = 0.678050239 Simplifying X = 0.678050239Subproblem 2
X + 1.361111111 = -2.03916135 Simplifying X + 1.361111111 = -2.03916135 Reorder the terms: 1.361111111 + X = -2.03916135 Solving 1.361111111 + X = -2.03916135 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.361111111' to each side of the equation. 1.361111111 + -1.361111111 + X = -2.03916135 + -1.361111111 Combine like terms: 1.361111111 + -1.361111111 = 0.000000000 0.000000000 + X = -2.03916135 + -1.361111111 X = -2.03916135 + -1.361111111 Combine like terms: -2.03916135 + -1.361111111 = -3.400272461 X = -3.400272461 Simplifying X = -3.400272461Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.678050239, -3.400272461}
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