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Simplifying X2 + -18X = -8 Reorder the terms: -18X + X2 = -8 Solving -18X + X2 = -8 Solving for variable 'X'. Reorder the terms: 8 + -18X + X2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + -18X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -18X + -8 + X2 = 0 + -8 Reorder the terms: 8 + -8 + -18X + X2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -18X + X2 = 0 + -8 -18X + X2 = 0 + -8 Combine like terms: 0 + -8 = -8 -18X + X2 = -8 The X term is -18X. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18X + 81 + X2 = -8 + 81 Reorder the terms: 81 + -18X + X2 = -8 + 81 Combine like terms: -8 + 81 = 73 81 + -18X + X2 = 73 Factor a perfect square on the left side: (X + -9)(X + -9) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (X + -9) equal to 8.544003745 and -8.544003745.Subproblem 1
X + -9 = 8.544003745 Simplifying X + -9 = 8.544003745 Reorder the terms: -9 + X = 8.544003745 Solving -9 + X = 8.544003745 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + X = 8.544003745 + 9 Combine like terms: -9 + 9 = 0 0 + X = 8.544003745 + 9 X = 8.544003745 + 9 Combine like terms: 8.544003745 + 9 = 17.544003745 X = 17.544003745 Simplifying X = 17.544003745Subproblem 2
X + -9 = -8.544003745 Simplifying X + -9 = -8.544003745 Reorder the terms: -9 + X = -8.544003745 Solving -9 + X = -8.544003745 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + X = -8.544003745 + 9 Combine like terms: -9 + 9 = 0 0 + X = -8.544003745 + 9 X = -8.544003745 + 9 Combine like terms: -8.544003745 + 9 = 0.455996255 X = 0.455996255 Simplifying X = 0.455996255Solution
The solution to the problem is based on the solutions from the subproblems. X = {17.544003745, 0.455996255}
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