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Simplifying x2 + 18x = 1 Reorder the terms: 18x + x2 = 1 Solving 18x + x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 18x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 18x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 18x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 18x + x2 = 0 + 1 18x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 18x + x2 = 1 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 = 1 + 81 Reorder the terms: 81 + 18x + x2 = 1 + 81 Combine like terms: 1 + 81 = 82 81 + 18x + x2 = 82 Factor a perfect square on the left side: (x + 9)(x + 9) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (x + 9) equal to 9.055385138 and -9.055385138.Subproblem 1
x + 9 = 9.055385138 Simplifying x + 9 = 9.055385138 Reorder the terms: 9 + x = 9.055385138 Solving 9 + x = 9.055385138 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 = 9.055385138 + -9 Combine like terms: 9 + -9 = 0 0 + x = 9.055385138 + -9 x = 9.055385138 + -9 Combine like terms: 9.055385138 + -9 = 0.055385138 x = 0.055385138 Simplifying x = 0.055385138Subproblem 2
x + 9 = -9.055385138 Simplifying x + 9 = -9.055385138 Reorder the terms: 9 + x = -9.055385138 Solving 9 + x = -9.055385138 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 = -9.055385138 + -9 Combine like terms: 9 + -9 = 0 0 + x = -9.055385138 + -9 x = -9.055385138 + -9 Combine like terms: -9.055385138 + -9 = -18.055385138 x = -18.055385138 Simplifying x = -18.055385138Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.055385138, -18.055385138}
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