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Simplifying x2 + 18x = 44 Reorder the terms: 18x + x2 = 44 Solving 18x + x2 = 44 Solving for variable 'x'. Reorder the terms: -44 + 18x + x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 18x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + 18x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 18x + x2 = 0 + 44 18x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 18x + x2 = 44 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 = 44 + 81 Reorder the terms: 81 + 18x + x2 = 44 + 81 Combine like terms: 44 + 81 = 125 81 + 18x + x2 = 125 Factor a perfect square on the left side: (x + 9)(x + 9) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + 9) equal to 11.180339887 and -11.180339887.Subproblem 1
x + 9 = 11.180339887 Simplifying x + 9 = 11.180339887 Reorder the terms: 9 + x = 11.180339887 Solving 9 + x = 11.180339887 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 = 11.180339887 + -9 Combine like terms: 9 + -9 = 0 0 + x = 11.180339887 + -9 x = 11.180339887 + -9 Combine like terms: 11.180339887 + -9 = 2.180339887 x = 2.180339887 Simplifying x = 2.180339887Subproblem 2
x + 9 = -11.180339887 Simplifying x + 9 = -11.180339887 Reorder the terms: 9 + x = -11.180339887 Solving 9 + x = -11.180339887 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 = -11.180339887 + -9 Combine like terms: 9 + -9 = 0 0 + x = -11.180339887 + -9 x = -11.180339887 + -9 Combine like terms: -11.180339887 + -9 = -20.180339887 x = -20.180339887 Simplifying x = -20.180339887Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.180339887, -20.180339887}
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