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Simplifying x(x + 6) = 320 Reorder the terms: x(6 + x) = 320 (6 * x + x * x) = 320 (6x + x2) = 320 Solving 6x + x2 = 320 Solving for variable 'x'. Reorder the terms: -320 + 6x + x2 = 320 + -320 Combine like terms: 320 + -320 = 0 -320 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '320' to each side of the equation. -320 + 6x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + 6x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + 6x + x2 = 0 + 320 6x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 6x + x2 = 320 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 = 320 + 9 Reorder the terms: 9 + 6x + x2 = 320 + 9 Combine like terms: 320 + 9 = 329 9 + 6x + x2 = 329 Factor a perfect square on the left side: (x + 3)(x + 3) = 329 Calculate the square root of the right side: 18.138357147 Break this problem into two subproblems by setting (x + 3) equal to 18.138357147 and -18.138357147.Subproblem 1
x + 3 = 18.138357147 Simplifying x + 3 = 18.138357147 Reorder the terms: 3 + x = 18.138357147 Solving 3 + x = 18.138357147 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 = 18.138357147 + -3 Combine like terms: 3 + -3 = 0 0 + x = 18.138357147 + -3 x = 18.138357147 + -3 Combine like terms: 18.138357147 + -3 = 15.138357147 x = 15.138357147 Simplifying x = 15.138357147Subproblem 2
x + 3 = -18.138357147 Simplifying x + 3 = -18.138357147 Reorder the terms: 3 + x = -18.138357147 Solving 3 + x = -18.138357147 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 = -18.138357147 + -3 Combine like terms: 3 + -3 = 0 0 + x = -18.138357147 + -3 x = -18.138357147 + -3 Combine like terms: -18.138357147 + -3 = -21.138357147 x = -21.138357147 Simplifying x = -21.138357147Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.138357147, -21.138357147}
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