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Simplifying x2 + 12x + -114 = 0 Reorder the terms: -114 + 12x + x2 = 0 Solving -114 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '114' to each side of the equation. -114 + 12x + 114 + x2 = 0 + 114 Reorder the terms: -114 + 114 + 12x + x2 = 0 + 114 Combine like terms: -114 + 114 = 0 0 + 12x + x2 = 0 + 114 12x + x2 = 0 + 114 Combine like terms: 0 + 114 = 114 12x + x2 = 114 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 = 114 + 36 Reorder the terms: 36 + 12x + x2 = 114 + 36 Combine like terms: 114 + 36 = 150 36 + 12x + x2 = 150 Factor a perfect square on the left side: (x + 6)(x + 6) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (x + 6) equal to 12.247448714 and -12.247448714.Subproblem 1
x + 6 = 12.247448714 Simplifying x + 6 = 12.247448714 Reorder the terms: 6 + x = 12.247448714 Solving 6 + x = 12.247448714 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 = 12.247448714 + -6 Combine like terms: 6 + -6 = 0 0 + x = 12.247448714 + -6 x = 12.247448714 + -6 Combine like terms: 12.247448714 + -6 = 6.247448714 x = 6.247448714 Simplifying x = 6.247448714Subproblem 2
x + 6 = -12.247448714 Simplifying x + 6 = -12.247448714 Reorder the terms: 6 + x = -12.247448714 Solving 6 + x = -12.247448714 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 = -12.247448714 + -6 Combine like terms: 6 + -6 = 0 0 + x = -12.247448714 + -6 x = -12.247448714 + -6 Combine like terms: -12.247448714 + -6 = -18.247448714 x = -18.247448714 Simplifying x = -18.247448714Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.247448714, -18.247448714}
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