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Simplifying x2 + 24x + -325 = 0 Reorder the terms: -325 + 24x + x2 = 0 Solving -325 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '325' to each side of the equation. -325 + 24x + 325 + x2 = 0 + 325 Reorder the terms: -325 + 325 + 24x + x2 = 0 + 325 Combine like terms: -325 + 325 = 0 0 + 24x + x2 = 0 + 325 24x + x2 = 0 + 325 Combine like terms: 0 + 325 = 325 24x + x2 = 325 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 = 325 + 144 Reorder the terms: 144 + 24x + x2 = 325 + 144 Combine like terms: 325 + 144 = 469 144 + 24x + x2 = 469 Factor a perfect square on the left side: (x + 12)(x + 12) = 469 Calculate the square root of the right side: 21.656407828 Break this problem into two subproblems by setting (x + 12) equal to 21.656407828 and -21.656407828.Subproblem 1
x + 12 = 21.656407828 Simplifying x + 12 = 21.656407828 Reorder the terms: 12 + x = 21.656407828 Solving 12 + x = 21.656407828 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 = 21.656407828 + -12 Combine like terms: 12 + -12 = 0 0 + x = 21.656407828 + -12 x = 21.656407828 + -12 Combine like terms: 21.656407828 + -12 = 9.656407828 x = 9.656407828 Simplifying x = 9.656407828Subproblem 2
x + 12 = -21.656407828 Simplifying x + 12 = -21.656407828 Reorder the terms: 12 + x = -21.656407828 Solving 12 + x = -21.656407828 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 = -21.656407828 + -12 Combine like terms: 12 + -12 = 0 0 + x = -21.656407828 + -12 x = -21.656407828 + -12 Combine like terms: -21.656407828 + -12 = -33.656407828 x = -33.656407828 Simplifying x = -33.656407828Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.656407828, -33.656407828}
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