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Simplifying x2 + 24x + 126 = 0 Reorder the terms: 126 + 24x + x2 = 0 Solving 126 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-126' to each side of the equation. 126 + 24x + -126 + x2 = 0 + -126 Reorder the terms: 126 + -126 + 24x + x2 = 0 + -126 Combine like terms: 126 + -126 = 0 0 + 24x + x2 = 0 + -126 24x + x2 = 0 + -126 Combine like terms: 0 + -126 = -126 24x + x2 = -126 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 = -126 + 144 Reorder the terms: 144 + 24x + x2 = -126 + 144 Combine like terms: -126 + 144 = 18 144 + 24x + x2 = 18 Factor a perfect square on the left side: (x + 12)(x + 12) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + 12) equal to 4.242640687 and -4.242640687.Subproblem 1
x + 12 = 4.242640687 Simplifying x + 12 = 4.242640687 Reorder the terms: 12 + x = 4.242640687 Solving 12 + x = 4.242640687 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 = 4.242640687 + -12 Combine like terms: 12 + -12 = 0 0 + x = 4.242640687 + -12 x = 4.242640687 + -12 Combine like terms: 4.242640687 + -12 = -7.757359313 x = -7.757359313 Simplifying x = -7.757359313Subproblem 2
x + 12 = -4.242640687 Simplifying x + 12 = -4.242640687 Reorder the terms: 12 + x = -4.242640687 Solving 12 + x = -4.242640687 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 = -4.242640687 + -12 Combine like terms: 12 + -12 = 0 0 + x = -4.242640687 + -12 x = -4.242640687 + -12 Combine like terms: -4.242640687 + -12 = -16.242640687 x = -16.242640687 Simplifying x = -16.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.757359313, -16.242640687}
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