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Simplifying x2 + 24x + -360 = 0 Reorder the terms: -360 + 24x + x2 = 0 Solving -360 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + 24x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 24x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 24x + x2 = 0 + 360 24x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 24x + x2 = 360 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 360 + 144 Reorder the terms: 144 + 24x + x2 = 360 + 144 Combine like terms: 360 + 144 = 504 144 + 24x + x2 = 504 Factor a perfect square on the left side: (x + 12)(x + 12) = 504 Calculate the square root of the right side: 22.449944321 Break this problem into two subproblems by setting (x + 12) equal to 22.449944321 and -22.449944321.Subproblem 1
x + 12 = 22.449944321 Simplifying x + 12 = 22.449944321 Reorder the terms: 12 + x = 22.449944321 Solving 12 + x = 22.449944321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 22.449944321 + -12 Combine like terms: 12 + -12 = 0 0 + x = 22.449944321 + -12 x = 22.449944321 + -12 Combine like terms: 22.449944321 + -12 = 10.449944321 x = 10.449944321 Simplifying x = 10.449944321Subproblem 2
x + 12 = -22.449944321 Simplifying x + 12 = -22.449944321 Reorder the terms: 12 + x = -22.449944321 Solving 12 + x = -22.449944321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -22.449944321 + -12 Combine like terms: 12 + -12 = 0 0 + x = -22.449944321 + -12 x = -22.449944321 + -12 Combine like terms: -22.449944321 + -12 = -34.449944321 x = -34.449944321 Simplifying x = -34.449944321Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.449944321, -34.449944321}
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