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Simplifying x2 + -18x + -324 = 0 Reorder the terms: -324 + -18x + x2 = 0 Solving -324 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '324' to each side of the equation. -324 + -18x + 324 + x2 = 0 + 324 Reorder the terms: -324 + 324 + -18x + x2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + -18x + x2 = 0 + 324 -18x + x2 = 0 + 324 Combine like terms: 0 + 324 = 324 -18x + x2 = 324 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 = 324 + 81 Reorder the terms: 81 + -18x + x2 = 324 + 81 Combine like terms: 324 + 81 = 405 81 + -18x + x2 = 405 Factor a perfect square on the left side: (x + -9)(x + -9) = 405 Calculate the square root of the right side: 20.124611797 Break this problem into two subproblems by setting (x + -9) equal to 20.124611797 and -20.124611797.Subproblem 1
x + -9 = 20.124611797 Simplifying x + -9 = 20.124611797 Reorder the terms: -9 + x = 20.124611797 Solving -9 + x = 20.124611797 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 = 20.124611797 + 9 Combine like terms: -9 + 9 = 0 0 + x = 20.124611797 + 9 x = 20.124611797 + 9 Combine like terms: 20.124611797 + 9 = 29.124611797 x = 29.124611797 Simplifying x = 29.124611797Subproblem 2
x + -9 = -20.124611797 Simplifying x + -9 = -20.124611797 Reorder the terms: -9 + x = -20.124611797 Solving -9 + x = -20.124611797 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 = -20.124611797 + 9 Combine like terms: -9 + 9 = 0 0 + x = -20.124611797 + 9 x = -20.124611797 + 9 Combine like terms: -20.124611797 + 9 = -11.124611797 x = -11.124611797 Simplifying x = -11.124611797Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.124611797, -11.124611797}
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