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Simplifying x(x + 6) = 168 Reorder the terms: x(6 + x) = 168 (6 * x + x * x) = 168 (6x + x2) = 168 Solving 6x + x2 = 168 Solving for variable 'x'. Reorder the terms: -168 + 6x + x2 = 168 + -168 Combine like terms: 168 + -168 = 0 -168 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '168' to each side of the equation. -168 + 6x + 168 + x2 = 0 + 168 Reorder the terms: -168 + 168 + 6x + x2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + 6x + x2 = 0 + 168 6x + x2 = 0 + 168 Combine like terms: 0 + 168 = 168 6x + x2 = 168 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 = 168 + 9 Reorder the terms: 9 + 6x + x2 = 168 + 9 Combine like terms: 168 + 9 = 177 9 + 6x + x2 = 177 Factor a perfect square on the left side: (x + 3)(x + 3) = 177 Calculate the square root of the right side: 13.304134696 Break this problem into two subproblems by setting (x + 3) equal to 13.304134696 and -13.304134696.Subproblem 1
x + 3 = 13.304134696 Simplifying x + 3 = 13.304134696 Reorder the terms: 3 + x = 13.304134696 Solving 3 + x = 13.304134696 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 = 13.304134696 + -3 Combine like terms: 3 + -3 = 0 0 + x = 13.304134696 + -3 x = 13.304134696 + -3 Combine like terms: 13.304134696 + -3 = 10.304134696 x = 10.304134696 Simplifying x = 10.304134696Subproblem 2
x + 3 = -13.304134696 Simplifying x + 3 = -13.304134696 Reorder the terms: 3 + x = -13.304134696 Solving 3 + x = -13.304134696 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 = -13.304134696 + -3 Combine like terms: 3 + -3 = 0 0 + x = -13.304134696 + -3 x = -13.304134696 + -3 Combine like terms: -13.304134696 + -3 = -16.304134696 x = -16.304134696 Simplifying x = -16.304134696Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.304134696, -16.304134696}
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