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Simplifying x2 + 6x + -199 = 0 Reorder the terms: -199 + 6x + x2 = 0 Solving -199 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '199' to each side of the equation. -199 + 6x + 199 + x2 = 0 + 199 Reorder the terms: -199 + 199 + 6x + x2 = 0 + 199 Combine like terms: -199 + 199 = 0 0 + 6x + x2 = 0 + 199 6x + x2 = 0 + 199 Combine like terms: 0 + 199 = 199 6x + x2 = 199 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 = 199 + 9 Reorder the terms: 9 + 6x + x2 = 199 + 9 Combine like terms: 199 + 9 = 208 9 + 6x + x2 = 208 Factor a perfect square on the left side: (x + 3)(x + 3) = 208 Calculate the square root of the right side: 14.422205102 Break this problem into two subproblems by setting (x + 3) equal to 14.422205102 and -14.422205102.Subproblem 1
x + 3 = 14.422205102 Simplifying x + 3 = 14.422205102 Reorder the terms: 3 + x = 14.422205102 Solving 3 + x = 14.422205102 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 = 14.422205102 + -3 Combine like terms: 3 + -3 = 0 0 + x = 14.422205102 + -3 x = 14.422205102 + -3 Combine like terms: 14.422205102 + -3 = 11.422205102 x = 11.422205102 Simplifying x = 11.422205102Subproblem 2
x + 3 = -14.422205102 Simplifying x + 3 = -14.422205102 Reorder the terms: 3 + x = -14.422205102 Solving 3 + x = -14.422205102 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 = -14.422205102 + -3 Combine like terms: 3 + -3 = 0 0 + x = -14.422205102 + -3 x = -14.422205102 + -3 Combine like terms: -14.422205102 + -3 = -17.422205102 x = -17.422205102 Simplifying x = -17.422205102Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.422205102, -17.422205102}
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