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Simplifying 100X2 + 19630.02X + -5054731.33 = 0 Reorder the terms: -5054731.33 + 19630.02X + 100X2 = 0 Solving -5054731.33 + 19630.02X + 100X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -50547.3133 + 196.3002X + X2 = 0 Move the constant term to the right: Add '50547.3133' to each side of the equation. -50547.3133 + 196.3002X + 50547.3133 + X2 = 0 + 50547.3133 Reorder the terms: -50547.3133 + 50547.3133 + 196.3002X + X2 = 0 + 50547.3133 Combine like terms: -50547.3133 + 50547.3133 = 0.0000 0.0000 + 196.3002X + X2 = 0 + 50547.3133 196.3002X + X2 = 0 + 50547.3133 Combine like terms: 0 + 50547.3133 = 50547.3133 196.3002X + X2 = 50547.3133 The X term is 196.3002X. Take half its coefficient (98.1501). Square it (9633.442130) and add it to both sides. Add '9633.442130' to each side of the equation. 196.3002X + 9633.442130 + X2 = 50547.3133 + 9633.442130 Reorder the terms: 9633.442130 + 196.3002X + X2 = 50547.3133 + 9633.442130 Combine like terms: 50547.3133 + 9633.442130 = 60180.75543 9633.442130 + 196.3002X + X2 = 60180.75543 Factor a perfect square on the left side: (X + 98.1501)(X + 98.1501) = 60180.75543 Calculate the square root of the right side: 245.317662287 Break this problem into two subproblems by setting (X + 98.1501) equal to 245.317662287 and -245.317662287.Subproblem 1
X + 98.1501 = 245.317662287 Simplifying X + 98.1501 = 245.317662287 Reorder the terms: 98.1501 + X = 245.317662287 Solving 98.1501 + X = 245.317662287 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-98.1501' to each side of the equation. 98.1501 + -98.1501 + X = 245.317662287 + -98.1501 Combine like terms: 98.1501 + -98.1501 = 0.0000 0.0000 + X = 245.317662287 + -98.1501 X = 245.317662287 + -98.1501 Combine like terms: 245.317662287 + -98.1501 = 147.167562287 X = 147.167562287 Simplifying X = 147.167562287Subproblem 2
X + 98.1501 = -245.317662287 Simplifying X + 98.1501 = -245.317662287 Reorder the terms: 98.1501 + X = -245.317662287 Solving 98.1501 + X = -245.317662287 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-98.1501' to each side of the equation. 98.1501 + -98.1501 + X = -245.317662287 + -98.1501 Combine like terms: 98.1501 + -98.1501 = 0.0000 0.0000 + X = -245.317662287 + -98.1501 X = -245.317662287 + -98.1501 Combine like terms: -245.317662287 + -98.1501 = -343.467762287 X = -343.467762287 Simplifying X = -343.467762287Solution
The solution to the problem is based on the solutions from the subproblems. X = {147.167562287, -343.467762287}
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