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Simplifying x2 + 18x = 1092 Reorder the terms: 18x + x2 = 1092 Solving 18x + x2 = 1092 Solving for variable 'x'. Reorder the terms: -1092 + 18x + x2 = 1092 + -1092 Combine like terms: 1092 + -1092 = 0 -1092 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1092' to each side of the equation. -1092 + 18x + 1092 + x2 = 0 + 1092 Reorder the terms: -1092 + 1092 + 18x + x2 = 0 + 1092 Combine like terms: -1092 + 1092 = 0 0 + 18x + x2 = 0 + 1092 18x + x2 = 0 + 1092 Combine like terms: 0 + 1092 = 1092 18x + x2 = 1092 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 = 1092 + 81 Reorder the terms: 81 + 18x + x2 = 1092 + 81 Combine like terms: 1092 + 81 = 1173 81 + 18x + x2 = 1173 Factor a perfect square on the left side: (x + 9)(x + 9) = 1173 Calculate the square root of the right side: 34.249087579 Break this problem into two subproblems by setting (x + 9) equal to 34.249087579 and -34.249087579.Subproblem 1
x + 9 = 34.249087579 Simplifying x + 9 = 34.249087579 Reorder the terms: 9 + x = 34.249087579 Solving 9 + x = 34.249087579 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 = 34.249087579 + -9 Combine like terms: 9 + -9 = 0 0 + x = 34.249087579 + -9 x = 34.249087579 + -9 Combine like terms: 34.249087579 + -9 = 25.249087579 x = 25.249087579 Simplifying x = 25.249087579Subproblem 2
x + 9 = -34.249087579 Simplifying x + 9 = -34.249087579 Reorder the terms: 9 + x = -34.249087579 Solving 9 + x = -34.249087579 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 = -34.249087579 + -9 Combine like terms: 9 + -9 = 0 0 + x = -34.249087579 + -9 x = -34.249087579 + -9 Combine like terms: -34.249087579 + -9 = -43.249087579 x = -43.249087579 Simplifying x = -43.249087579Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.249087579, -43.249087579}
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