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Simplifying x2 + 12x + -126 = 0 Reorder the terms: -126 + 12x + x2 = 0 Solving -126 + 12x + 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 + 12x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + 12x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + 12x + x2 = 0 + 126 12x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 12x + x2 = 126 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 = 126 + 36 Reorder the terms: 36 + 12x + x2 = 126 + 36 Combine like terms: 126 + 36 = 162 36 + 12x + x2 = 162 Factor a perfect square on the left side: (x + 6)(x + 6) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (x + 6) equal to 12.727922061 and -12.727922061.Subproblem 1
x + 6 = 12.727922061 Simplifying x + 6 = 12.727922061 Reorder the terms: 6 + x = 12.727922061 Solving 6 + x = 12.727922061 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 = 12.727922061 + -6 Combine like terms: 6 + -6 = 0 0 + x = 12.727922061 + -6 x = 12.727922061 + -6 Combine like terms: 12.727922061 + -6 = 6.727922061 x = 6.727922061 Simplifying x = 6.727922061Subproblem 2
x + 6 = -12.727922061 Simplifying x + 6 = -12.727922061 Reorder the terms: 6 + x = -12.727922061 Solving 6 + x = -12.727922061 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 = -12.727922061 + -6 Combine like terms: 6 + -6 = 0 0 + x = -12.727922061 + -6 x = -12.727922061 + -6 Combine like terms: -12.727922061 + -6 = -18.727922061 x = -18.727922061 Simplifying x = -18.727922061Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.727922061, -18.727922061}
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