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Simplifying (x + 6)(x + 6) = 296 Reorder the terms: (6 + x)(x + 6) = 296 Reorder the terms: (6 + x)(6 + x) = 296 Multiply (6 + x) * (6 + x) (6(6 + x) + x(6 + x)) = 296 ((6 * 6 + x * 6) + x(6 + x)) = 296 ((36 + 6x) + x(6 + x)) = 296 (36 + 6x + (6 * x + x * x)) = 296 (36 + 6x + (6x + x2)) = 296 Combine like terms: 6x + 6x = 12x (36 + 12x + x2) = 296 Solving 36 + 12x + x2 = 296 Solving for variable 'x'. Reorder the terms: 36 + -296 + 12x + x2 = 296 + -296 Combine like terms: 36 + -296 = -260 -260 + 12x + x2 = 296 + -296 Combine like terms: 296 + -296 = 0 -260 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '260' to each side of the equation. -260 + 12x + 260 + x2 = 0 + 260 Reorder the terms: -260 + 260 + 12x + x2 = 0 + 260 Combine like terms: -260 + 260 = 0 0 + 12x + x2 = 0 + 260 12x + x2 = 0 + 260 Combine like terms: 0 + 260 = 260 12x + x2 = 260 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 260 + 36 Reorder the terms: 36 + 12x + x2 = 260 + 36 Combine like terms: 260 + 36 = 296 36 + 12x + x2 = 296 Factor a perfect square on the left side: (x + 6)(x + 6) = 296 Calculate the square root of the right side: 17.204650534 Break this problem into two subproblems by setting (x + 6) equal to 17.204650534 and -17.204650534.Subproblem 1
x + 6 = 17.204650534 Simplifying x + 6 = 17.204650534 Reorder the terms: 6 + x = 17.204650534 Solving 6 + x = 17.204650534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 17.204650534 + -6 Combine like terms: 6 + -6 = 0 0 + x = 17.204650534 + -6 x = 17.204650534 + -6 Combine like terms: 17.204650534 + -6 = 11.204650534 x = 11.204650534 Simplifying x = 11.204650534Subproblem 2
x + 6 = -17.204650534 Simplifying x + 6 = -17.204650534 Reorder the terms: 6 + x = -17.204650534 Solving 6 + x = -17.204650534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -17.204650534 + -6 Combine like terms: 6 + -6 = 0 0 + x = -17.204650534 + -6 x = -17.204650534 + -6 Combine like terms: -17.204650534 + -6 = -23.204650534 x = -23.204650534 Simplifying x = -23.204650534Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.204650534, -23.204650534}
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