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Simplifying x2 + 6x + -118 = 0 Reorder the terms: -118 + 6x + x2 = 0 Solving -118 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '118' to each side of the equation. -118 + 6x + 118 + x2 = 0 + 118 Reorder the terms: -118 + 118 + 6x + x2 = 0 + 118 Combine like terms: -118 + 118 = 0 0 + 6x + x2 = 0 + 118 6x + x2 = 0 + 118 Combine like terms: 0 + 118 = 118 6x + x2 = 118 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 = 118 + 9 Reorder the terms: 9 + 6x + x2 = 118 + 9 Combine like terms: 118 + 9 = 127 9 + 6x + x2 = 127 Factor a perfect square on the left side: (x + 3)(x + 3) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (x + 3) equal to 11.26942767 and -11.26942767.Subproblem 1
x + 3 = 11.26942767 Simplifying x + 3 = 11.26942767 Reorder the terms: 3 + x = 11.26942767 Solving 3 + x = 11.26942767 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 = 11.26942767 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.26942767 + -3 x = 11.26942767 + -3 Combine like terms: 11.26942767 + -3 = 8.26942767 x = 8.26942767 Simplifying x = 8.26942767Subproblem 2
x + 3 = -11.26942767 Simplifying x + 3 = -11.26942767 Reorder the terms: 3 + x = -11.26942767 Solving 3 + x = -11.26942767 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 = -11.26942767 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.26942767 + -3 x = -11.26942767 + -3 Combine like terms: -11.26942767 + -3 = -14.26942767 x = -14.26942767 Simplifying x = -14.26942767Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.26942767, -14.26942767}
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