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Simplifying x2 + 18x = 18 Reorder the terms: 18x + x2 = 18 Solving 18x + x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + 18x + x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 18x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 18x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 18x + x2 = 0 + 18 18x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 18x + x2 = 18 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 = 18 + 81 Reorder the terms: 81 + 18x + x2 = 18 + 81 Combine like terms: 18 + 81 = 99 81 + 18x + x2 = 99 Factor a perfect square on the left side: (x + 9)(x + 9) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x + 9) equal to 9.949874371 and -9.949874371.Subproblem 1
x + 9 = 9.949874371 Simplifying x + 9 = 9.949874371 Reorder the terms: 9 + x = 9.949874371 Solving 9 + x = 9.949874371 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 = 9.949874371 + -9 Combine like terms: 9 + -9 = 0 0 + x = 9.949874371 + -9 x = 9.949874371 + -9 Combine like terms: 9.949874371 + -9 = 0.949874371 x = 0.949874371 Simplifying x = 0.949874371Subproblem 2
x + 9 = -9.949874371 Simplifying x + 9 = -9.949874371 Reorder the terms: 9 + x = -9.949874371 Solving 9 + x = -9.949874371 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 = -9.949874371 + -9 Combine like terms: 9 + -9 = 0 0 + x = -9.949874371 + -9 x = -9.949874371 + -9 Combine like terms: -9.949874371 + -9 = -18.949874371 x = -18.949874371 Simplifying x = -18.949874371Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.949874371, -18.949874371}
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