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Simplifying x2 + 6x + -114 = 0 Reorder the terms: -114 + 6x + x2 = 0 Solving -114 + 6x + 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 + 6x + 114 + x2 = 0 + 114 Reorder the terms: -114 + 114 + 6x + x2 = 0 + 114 Combine like terms: -114 + 114 = 0 0 + 6x + x2 = 0 + 114 6x + x2 = 0 + 114 Combine like terms: 0 + 114 = 114 6x + x2 = 114 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 114 + 9 Reorder the terms: 9 + 6x + x2 = 114 + 9 Combine like terms: 114 + 9 = 123 9 + 6x + x2 = 123 Factor a perfect square on the left side: (x + 3)(x + 3) = 123 Calculate the square root of the right side: 11.090536506 Break this problem into two subproblems by setting (x + 3) equal to 11.090536506 and -11.090536506.Subproblem 1
x + 3 = 11.090536506 Simplifying x + 3 = 11.090536506 Reorder the terms: 3 + x = 11.090536506 Solving 3 + x = 11.090536506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 11.090536506 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.090536506 + -3 x = 11.090536506 + -3 Combine like terms: 11.090536506 + -3 = 8.090536506 x = 8.090536506 Simplifying x = 8.090536506Subproblem 2
x + 3 = -11.090536506 Simplifying x + 3 = -11.090536506 Reorder the terms: 3 + x = -11.090536506 Solving 3 + x = -11.090536506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -11.090536506 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.090536506 + -3 x = -11.090536506 + -3 Combine like terms: -11.090536506 + -3 = -14.090536506 x = -14.090536506 Simplifying x = -14.090536506Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.090536506, -14.090536506}
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