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Simplifying x2 + -18x + -9 = 29 Reorder the terms: -9 + -18x + x2 = 29 Solving -9 + -18x + x2 = 29 Solving for variable 'x'. Reorder the terms: -9 + -29 + -18x + x2 = 29 + -29 Combine like terms: -9 + -29 = -38 -38 + -18x + x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -38 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + -18x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + -18x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -18x + x2 = 0 + 38 -18x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 -18x + x2 = 38 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 = 38 + 81 Reorder the terms: 81 + -18x + x2 = 38 + 81 Combine like terms: 38 + 81 = 119 81 + -18x + x2 = 119 Factor a perfect square on the left side: (x + -9)(x + -9) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (x + -9) equal to 10.908712115 and -10.908712115.Subproblem 1
x + -9 = 10.908712115 Simplifying x + -9 = 10.908712115 Reorder the terms: -9 + x = 10.908712115 Solving -9 + x = 10.908712115 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 = 10.908712115 + 9 Combine like terms: -9 + 9 = 0 0 + x = 10.908712115 + 9 x = 10.908712115 + 9 Combine like terms: 10.908712115 + 9 = 19.908712115 x = 19.908712115 Simplifying x = 19.908712115Subproblem 2
x + -9 = -10.908712115 Simplifying x + -9 = -10.908712115 Reorder the terms: -9 + x = -10.908712115 Solving -9 + x = -10.908712115 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 = -10.908712115 + 9 Combine like terms: -9 + 9 = 0 0 + x = -10.908712115 + 9 x = -10.908712115 + 9 Combine like terms: -10.908712115 + 9 = -1.908712115 x = -1.908712115 Simplifying x = -1.908712115Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.908712115, -1.908712115}
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