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Simplifying x2 = 18x + 53 Reorder the terms: x2 = 53 + 18x Solving x2 = 53 + 18x Solving for variable 'x'. Reorder the terms: -53 + -18x + x2 = 53 + 18x + -53 + -18x Reorder the terms: -53 + -18x + x2 = 53 + -53 + 18x + -18x Combine like terms: 53 + -53 = 0 -53 + -18x + x2 = 0 + 18x + -18x -53 + -18x + x2 = 18x + -18x Combine like terms: 18x + -18x = 0 -53 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + -18x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + -18x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + -18x + x2 = 0 + 53 -18x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 -18x + x2 = 53 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 = 53 + 81 Reorder the terms: 81 + -18x + x2 = 53 + 81 Combine like terms: 53 + 81 = 134 81 + -18x + x2 = 134 Factor a perfect square on the left side: (x + -9)(x + -9) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (x + -9) equal to 11.575836903 and -11.575836903.Subproblem 1
x + -9 = 11.575836903 Simplifying x + -9 = 11.575836903 Reorder the terms: -9 + x = 11.575836903 Solving -9 + x = 11.575836903 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 = 11.575836903 + 9 Combine like terms: -9 + 9 = 0 0 + x = 11.575836903 + 9 x = 11.575836903 + 9 Combine like terms: 11.575836903 + 9 = 20.575836903 x = 20.575836903 Simplifying x = 20.575836903Subproblem 2
x + -9 = -11.575836903 Simplifying x + -9 = -11.575836903 Reorder the terms: -9 + x = -11.575836903 Solving -9 + x = -11.575836903 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 = -11.575836903 + 9 Combine like terms: -9 + 9 = 0 0 + x = -11.575836903 + 9 x = -11.575836903 + 9 Combine like terms: -11.575836903 + 9 = -2.575836903 x = -2.575836903 Simplifying x = -2.575836903Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.575836903, -2.575836903}
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