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Simplifying x2 + 9x + -324 = 0 Reorder the terms: -324 + 9x + x2 = 0 Solving -324 + 9x + 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 + 9x + 324 + x2 = 0 + 324 Reorder the terms: -324 + 324 + 9x + x2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + 9x + x2 = 0 + 324 9x + x2 = 0 + 324 Combine like terms: 0 + 324 = 324 9x + x2 = 324 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 324 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 324 + 20.25 Combine like terms: 324 + 20.25 = 344.25 20.25 + 9x + x2 = 344.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 344.25 Calculate the square root of the right side: 18.553975315 Break this problem into two subproblems by setting (x + 4.5) equal to 18.553975315 and -18.553975315.Subproblem 1
x + 4.5 = 18.553975315 Simplifying x + 4.5 = 18.553975315 Reorder the terms: 4.5 + x = 18.553975315 Solving 4.5 + x = 18.553975315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 18.553975315 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 18.553975315 + -4.5 x = 18.553975315 + -4.5 Combine like terms: 18.553975315 + -4.5 = 14.053975315 x = 14.053975315 Simplifying x = 14.053975315Subproblem 2
x + 4.5 = -18.553975315 Simplifying x + 4.5 = -18.553975315 Reorder the terms: 4.5 + x = -18.553975315 Solving 4.5 + x = -18.553975315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -18.553975315 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -18.553975315 + -4.5 x = -18.553975315 + -4.5 Combine like terms: -18.553975315 + -4.5 = -23.053975315 x = -23.053975315 Simplifying x = -23.053975315Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.053975315, -23.053975315}
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