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Simplifying x2 + 24x + 142 = 0 Reorder the terms: 142 + 24x + x2 = 0 Solving 142 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-142' to each side of the equation. 142 + 24x + -142 + x2 = 0 + -142 Reorder the terms: 142 + -142 + 24x + x2 = 0 + -142 Combine like terms: 142 + -142 = 0 0 + 24x + x2 = 0 + -142 24x + x2 = 0 + -142 Combine like terms: 0 + -142 = -142 24x + x2 = -142 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 = -142 + 144 Reorder the terms: 144 + 24x + x2 = -142 + 144 Combine like terms: -142 + 144 = 2 144 + 24x + x2 = 2 Factor a perfect square on the left side: (x + 12)(x + 12) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 12) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 12 = 1.414213562 Simplifying x + 12 = 1.414213562 Reorder the terms: 12 + x = 1.414213562 Solving 12 + x = 1.414213562 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 = 1.414213562 + -12 Combine like terms: 12 + -12 = 0 0 + x = 1.414213562 + -12 x = 1.414213562 + -12 Combine like terms: 1.414213562 + -12 = -10.585786438 x = -10.585786438 Simplifying x = -10.585786438Subproblem 2
x + 12 = -1.414213562 Simplifying x + 12 = -1.414213562 Reorder the terms: 12 + x = -1.414213562 Solving 12 + x = -1.414213562 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 = -1.414213562 + -12 Combine like terms: 12 + -12 = 0 0 + x = -1.414213562 + -12 x = -1.414213562 + -12 Combine like terms: -1.414213562 + -12 = -13.414213562 x = -13.414213562 Simplifying x = -13.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.585786438, -13.414213562}
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