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Simplifying 0 = (x2 + 6x + -1184) Reorder the terms: 0 = (-1184 + 6x + x2) Remove parenthesis around (-1184 + 6x + x2) 0 = -1184 + 6x + x2 Solving 0 = -1184 + 6x + x2 Solving for variable 'x'. Combine like terms: 0 + 1184 = 1184 1184 + -6x + -1x2 = -1184 + 6x + x2 + 1184 + -6x + -1x2 Reorder the terms: 1184 + -6x + -1x2 = -1184 + 1184 + 6x + -6x + x2 + -1x2 Combine like terms: -1184 + 1184 = 0 1184 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 1184 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 1184 + -6x + -1x2 = 0 + x2 + -1x2 1184 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1184 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1184 + 6x + x2 = 0 Move the constant term to the right: Add '1184' to each side of the equation. -1184 + 6x + 1184 + x2 = 0 + 1184 Reorder the terms: -1184 + 1184 + 6x + x2 = 0 + 1184 Combine like terms: -1184 + 1184 = 0 0 + 6x + x2 = 0 + 1184 6x + x2 = 0 + 1184 Combine like terms: 0 + 1184 = 1184 6x + x2 = 1184 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 = 1184 + 9 Reorder the terms: 9 + 6x + x2 = 1184 + 9 Combine like terms: 1184 + 9 = 1193 9 + 6x + x2 = 1193 Factor a perfect square on the left side: (x + 3)(x + 3) = 1193 Calculate the square root of the right side: 34.539832078 Break this problem into two subproblems by setting (x + 3) equal to 34.539832078 and -34.539832078.Subproblem 1
x + 3 = 34.539832078 Simplifying x + 3 = 34.539832078 Reorder the terms: 3 + x = 34.539832078 Solving 3 + x = 34.539832078 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 = 34.539832078 + -3 Combine like terms: 3 + -3 = 0 0 + x = 34.539832078 + -3 x = 34.539832078 + -3 Combine like terms: 34.539832078 + -3 = 31.539832078 x = 31.539832078 Simplifying x = 31.539832078Subproblem 2
x + 3 = -34.539832078 Simplifying x + 3 = -34.539832078 Reorder the terms: 3 + x = -34.539832078 Solving 3 + x = -34.539832078 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 = -34.539832078 + -3 Combine like terms: 3 + -3 = 0 0 + x = -34.539832078 + -3 x = -34.539832078 + -3 Combine like terms: -34.539832078 + -3 = -37.539832078 x = -37.539832078 Simplifying x = -37.539832078Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.539832078, -37.539832078}
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