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Simplifying x(x + 6) = 30 Reorder the terms: x(6 + x) = 30 (6 * x + x * x) = 30 (6x + x2) = 30 Solving 6x + x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 6x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 6x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 6x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 6x + x2 = 0 + 30 6x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 6x + x2 = 30 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 = 30 + 9 Reorder the terms: 9 + 6x + x2 = 30 + 9 Combine like terms: 30 + 9 = 39 9 + 6x + x2 = 39 Factor a perfect square on the left side: (x + 3)(x + 3) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + 3) equal to 6.244997998 and -6.244997998.Subproblem 1
x + 3 = 6.244997998 Simplifying x + 3 = 6.244997998 Reorder the terms: 3 + x = 6.244997998 Solving 3 + x = 6.244997998 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 = 6.244997998 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.244997998 + -3 x = 6.244997998 + -3 Combine like terms: 6.244997998 + -3 = 3.244997998 x = 3.244997998 Simplifying x = 3.244997998Subproblem 2
x + 3 = -6.244997998 Simplifying x + 3 = -6.244997998 Reorder the terms: 3 + x = -6.244997998 Solving 3 + x = -6.244997998 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 = -6.244997998 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.244997998 + -3 x = -6.244997998 + -3 Combine like terms: -6.244997998 + -3 = -9.244997998 x = -9.244997998 Simplifying x = -9.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.244997998, -9.244997998}
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