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Simplifying x2 + 18x = 248 Reorder the terms: 18x + x2 = 248 Solving 18x + x2 = 248 Solving for variable 'x'. Reorder the terms: -248 + 18x + x2 = 248 + -248 Combine like terms: 248 + -248 = 0 -248 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '248' to each side of the equation. -248 + 18x + 248 + x2 = 0 + 248 Reorder the terms: -248 + 248 + 18x + x2 = 0 + 248 Combine like terms: -248 + 248 = 0 0 + 18x + x2 = 0 + 248 18x + x2 = 0 + 248 Combine like terms: 0 + 248 = 248 18x + x2 = 248 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 = 248 + 81 Reorder the terms: 81 + 18x + x2 = 248 + 81 Combine like terms: 248 + 81 = 329 81 + 18x + x2 = 329 Factor a perfect square on the left side: (x + 9)(x + 9) = 329 Calculate the square root of the right side: 18.138357147 Break this problem into two subproblems by setting (x + 9) equal to 18.138357147 and -18.138357147.Subproblem 1
x + 9 = 18.138357147 Simplifying x + 9 = 18.138357147 Reorder the terms: 9 + x = 18.138357147 Solving 9 + x = 18.138357147 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 = 18.138357147 + -9 Combine like terms: 9 + -9 = 0 0 + x = 18.138357147 + -9 x = 18.138357147 + -9 Combine like terms: 18.138357147 + -9 = 9.138357147 x = 9.138357147 Simplifying x = 9.138357147Subproblem 2
x + 9 = -18.138357147 Simplifying x + 9 = -18.138357147 Reorder the terms: 9 + x = -18.138357147 Solving 9 + x = -18.138357147 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 = -18.138357147 + -9 Combine like terms: 9 + -9 = 0 0 + x = -18.138357147 + -9 x = -18.138357147 + -9 Combine like terms: -18.138357147 + -9 = -27.138357147 x = -27.138357147 Simplifying x = -27.138357147Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.138357147, -27.138357147}
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