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Simplifying x2 + 24x + -135 = 0 Reorder the terms: -135 + 24x + x2 = 0 Solving -135 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '135' to each side of the equation. -135 + 24x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + 24x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + 24x + x2 = 0 + 135 24x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 24x + x2 = 135 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 = 135 + 144 Reorder the terms: 144 + 24x + x2 = 135 + 144 Combine like terms: 135 + 144 = 279 144 + 24x + x2 = 279 Factor a perfect square on the left side: (x + 12)(x + 12) = 279 Calculate the square root of the right side: 16.703293088 Break this problem into two subproblems by setting (x + 12) equal to 16.703293088 and -16.703293088.Subproblem 1
x + 12 = 16.703293088 Simplifying x + 12 = 16.703293088 Reorder the terms: 12 + x = 16.703293088 Solving 12 + x = 16.703293088 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 = 16.703293088 + -12 Combine like terms: 12 + -12 = 0 0 + x = 16.703293088 + -12 x = 16.703293088 + -12 Combine like terms: 16.703293088 + -12 = 4.703293088 x = 4.703293088 Simplifying x = 4.703293088Subproblem 2
x + 12 = -16.703293088 Simplifying x + 12 = -16.703293088 Reorder the terms: 12 + x = -16.703293088 Solving 12 + x = -16.703293088 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 = -16.703293088 + -12 Combine like terms: 12 + -12 = 0 0 + x = -16.703293088 + -12 x = -16.703293088 + -12 Combine like terms: -16.703293088 + -12 = -28.703293088 x = -28.703293088 Simplifying x = -28.703293088Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.703293088, -28.703293088}
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