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Simplifying x2 + 12x + -98 = 0 Reorder the terms: -98 + 12x + x2 = 0 Solving -98 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + 12x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + 12x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + 12x + x2 = 0 + 98 12x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 12x + x2 = 98 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 98 + 36 Reorder the terms: 36 + 12x + x2 = 98 + 36 Combine like terms: 98 + 36 = 134 36 + 12x + x2 = 134 Factor a perfect square on the left side: (x + 6)(x + 6) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (x + 6) equal to 11.575836903 and -11.575836903.Subproblem 1
x + 6 = 11.575836903 Simplifying x + 6 = 11.575836903 Reorder the terms: 6 + x = 11.575836903 Solving 6 + x = 11.575836903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 11.575836903 + -6 Combine like terms: 6 + -6 = 0 0 + x = 11.575836903 + -6 x = 11.575836903 + -6 Combine like terms: 11.575836903 + -6 = 5.575836903 x = 5.575836903 Simplifying x = 5.575836903Subproblem 2
x + 6 = -11.575836903 Simplifying x + 6 = -11.575836903 Reorder the terms: 6 + x = -11.575836903 Solving 6 + x = -11.575836903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -11.575836903 + -6 Combine like terms: 6 + -6 = 0 0 + x = -11.575836903 + -6 x = -11.575836903 + -6 Combine like terms: -11.575836903 + -6 = -17.575836903 x = -17.575836903 Simplifying x = -17.575836903Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.575836903, -17.575836903}
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