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Simplifying 16.18 = ((0.16) * X2) + 25.04X + 6.452 Reorder the terms: 16.18 = 6.452 + 25.04X + (0.16X2) Solving 16.18 = 6.452 + 25.04X + (0.16X2) Solving for variable 'X'. Combine like terms: 16.18 + -6.452 = 9.728 9.728 + -25.04X + (-0.16X2) = 6.452 + 25.04X + (0.16X2) + -6.452 + -25.04X + (-0.16X2) Reorder the terms: 9.728 + -25.04X + (-0.16X2) = 6.452 + -6.452 + 25.04X + -25.04X + (0.16X2) + (-0.16X2) Combine like terms: 6.452 + -6.452 = 0.000 9.728 + -25.04X + (-0.16X2) = 0.000 + 25.04X + -25.04X + (0.16X2) + (-0.16X2) 9.728 + -25.04X + (-0.16X2) = 25.04X + -25.04X + (0.16X2) + (-0.16X2) Combine like terms: 25.04X + -25.04X = 0.00 9.728 + -25.04X + (-0.16X2) = 0.00 + (0.16X2) + (-0.16X2) 9.728 + -25.04X + (-0.16X2) = (0.16X2) + (-0.16X2) Combine like terms: (0.16X2) + (-0.16X2) = 0.00 9.728 + -25.04X + (-0.16X2) = 0.00 Begin completing the square. Divide all terms by -0.16 the coefficient of the squared term: Divide each side by '-0.16'. -60.8 + 156.5X + X2 = 0 Move the constant term to the right: Add '60.8' to each side of the equation. -60.8 + 156.5X + 60.8 + X2 = 0 + 60.8 Reorder the terms: -60.8 + 60.8 + 156.5X + X2 = 0 + 60.8 Combine like terms: -60.8 + 60.8 = 0.0 0.0 + 156.5X + X2 = 0 + 60.8 156.5X + X2 = 0 + 60.8 Combine like terms: 0 + 60.8 = 60.8 156.5X + X2 = 60.8 The X term is 156.5X. Take half its coefficient (78.25). Square it (6123.0625) and add it to both sides. Add '6123.0625' to each side of the equation. 156.5X + 6123.0625 + X2 = 60.8 + 6123.0625 Reorder the terms: 6123.0625 + 156.5X + X2 = 60.8 + 6123.0625 Combine like terms: 60.8 + 6123.0625 = 6183.8625 6123.0625 + 156.5X + X2 = 6183.8625 Factor a perfect square on the left side: ((X) + 78.25)((X) + 78.25) = 6183.8625 Calculate the square root of the right side: 78.637538746 Break this problem into two subproblems by setting ((X) + 78.25) equal to 78.637538746 and -78.637538746.Subproblem 1
(X) + 78.25 = 78.637538746 Simplifying (X) + 78.25 = 78.637538746 X + 78.25 = 78.637538746 Reorder the terms: 78.25 + X = 78.637538746 Solving 78.25 + X = 78.637538746 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-78.25' to each side of the equation. 78.25 + -78.25 + X = 78.637538746 + -78.25 Combine like terms: 78.25 + -78.25 = 0.00 0.00 + X = 78.637538746 + -78.25 X = 78.637538746 + -78.25 Combine like terms: 78.637538746 + -78.25 = 0.387538746 X = 0.387538746 Simplifying X = 0.387538746Subproblem 2
(X) + 78.25 = -78.637538746 Simplifying (X) + 78.25 = -78.637538746 X + 78.25 = -78.637538746 Reorder the terms: 78.25 + X = -78.637538746 Solving 78.25 + X = -78.637538746 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-78.25' to each side of the equation. 78.25 + -78.25 + X = -78.637538746 + -78.25 Combine like terms: 78.25 + -78.25 = 0.00 0.00 + X = -78.637538746 + -78.25 X = -78.637538746 + -78.25 Combine like terms: -78.637538746 + -78.25 = -156.887538746 X = -156.887538746 Simplifying X = -156.887538746Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.387538746, -156.887538746}
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