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Simplifying x2 + -18x + -18 = 2 Reorder the terms: -18 + -18x + x2 = 2 Solving -18 + -18x + x2 = 2 Solving for variable 'x'. Reorder the terms: -18 + -2 + -18x + x2 = 2 + -2 Combine like terms: -18 + -2 = -20 -20 + -18x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -20 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -18x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -18x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -18x + x2 = 0 + 20 -18x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -18x + x2 = 20 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 = 20 + 81 Reorder the terms: 81 + -18x + x2 = 20 + 81 Combine like terms: 20 + 81 = 101 81 + -18x + x2 = 101 Factor a perfect square on the left side: (x + -9)(x + -9) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + -9) equal to 10.049875621 and -10.049875621.Subproblem 1
x + -9 = 10.049875621 Simplifying x + -9 = 10.049875621 Reorder the terms: -9 + x = 10.049875621 Solving -9 + x = 10.049875621 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 = 10.049875621 + 9 Combine like terms: -9 + 9 = 0 0 + x = 10.049875621 + 9 x = 10.049875621 + 9 Combine like terms: 10.049875621 + 9 = 19.049875621 x = 19.049875621 Simplifying x = 19.049875621Subproblem 2
x + -9 = -10.049875621 Simplifying x + -9 = -10.049875621 Reorder the terms: -9 + x = -10.049875621 Solving -9 + x = -10.049875621 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 = -10.049875621 + 9 Combine like terms: -9 + 9 = 0 0 + x = -10.049875621 + 9 x = -10.049875621 + 9 Combine like terms: -10.049875621 + 9 = -1.049875621 x = -1.049875621 Simplifying x = -1.049875621Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.049875621, -1.049875621}
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