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Simplifying X = 3X(180 + -1X) + 8 X = (180 * 3X + -1X * 3X) + 8 X = (540X + -3X2) + 8 Reorder the terms: X = 8 + 540X + -3X2 Solving X = 8 + 540X + -3X2 Solving for variable 'X'. Reorder the terms: -8 + X + -540X + 3X2 = 8 + 540X + -3X2 + -8 + -540X + 3X2 Combine like terms: X + -540X = -539X -8 + -539X + 3X2 = 8 + 540X + -3X2 + -8 + -540X + 3X2 Reorder the terms: -8 + -539X + 3X2 = 8 + -8 + 540X + -540X + -3X2 + 3X2 Combine like terms: 8 + -8 = 0 -8 + -539X + 3X2 = 0 + 540X + -540X + -3X2 + 3X2 -8 + -539X + 3X2 = 540X + -540X + -3X2 + 3X2 Combine like terms: 540X + -540X = 0 -8 + -539X + 3X2 = 0 + -3X2 + 3X2 -8 + -539X + 3X2 = -3X2 + 3X2 Combine like terms: -3X2 + 3X2 = 0 -8 + -539X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + -179.6666667X + X2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -179.6666667X + 2.666666667 + X2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -179.6666667X + X2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -179.6666667X + X2 = 0 + 2.666666667 -179.6666667X + X2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -179.6666667X + X2 = 2.666666667 The X term is -179.6666667X. Take half its coefficient (-89.83333335). Square it (8070.027781) and add it to both sides. Add '8070.027781' to each side of the equation. -179.6666667X + 8070.027781 + X2 = 2.666666667 + 8070.027781 Reorder the terms: 8070.027781 + -179.6666667X + X2 = 2.666666667 + 8070.027781 Combine like terms: 2.666666667 + 8070.027781 = 8072.694447667 8070.027781 + -179.6666667X + X2 = 8072.694447667 Factor a perfect square on the left side: (X + -89.83333335)(X + -89.83333335) = 8072.694447667 Calculate the square root of the right side: 89.848174426 Break this problem into two subproblems by setting (X + -89.83333335) equal to 89.848174426 and -89.848174426.Subproblem 1
X + -89.83333335 = 89.848174426 Simplifying X + -89.83333335 = 89.848174426 Reorder the terms: -89.83333335 + X = 89.848174426 Solving -89.83333335 + X = 89.848174426 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '89.83333335' to each side of the equation. -89.83333335 + 89.83333335 + X = 89.848174426 + 89.83333335 Combine like terms: -89.83333335 + 89.83333335 = 0.00000000 0.00000000 + X = 89.848174426 + 89.83333335 X = 89.848174426 + 89.83333335 Combine like terms: 89.848174426 + 89.83333335 = 179.681507776 X = 179.681507776 Simplifying X = 179.681507776Subproblem 2
X + -89.83333335 = -89.848174426 Simplifying X + -89.83333335 = -89.848174426 Reorder the terms: -89.83333335 + X = -89.848174426 Solving -89.83333335 + X = -89.848174426 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '89.83333335' to each side of the equation. -89.83333335 + 89.83333335 + X = -89.848174426 + 89.83333335 Combine like terms: -89.83333335 + 89.83333335 = 0.00000000 0.00000000 + X = -89.848174426 + 89.83333335 X = -89.848174426 + 89.83333335 Combine like terms: -89.848174426 + 89.83333335 = -0.014841076 X = -0.014841076 Simplifying X = -0.014841076Solution
The solution to the problem is based on the solutions from the subproblems. X = {179.681507776, -0.014841076}
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