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Simplifying (x + 6)(x + 6) = 23 Reorder the terms: (6 + x)(x + 6) = 23 Reorder the terms: (6 + x)(6 + x) = 23 Multiply (6 + x) * (6 + x) (6(6 + x) + x(6 + x)) = 23 ((6 * 6 + x * 6) + x(6 + x)) = 23 ((36 + 6x) + x(6 + x)) = 23 (36 + 6x + (6 * x + x * x)) = 23 (36 + 6x + (6x + x2)) = 23 Combine like terms: 6x + 6x = 12x (36 + 12x + x2) = 23 Solving 36 + 12x + x2 = 23 Solving for variable 'x'. Reorder the terms: 36 + -23 + 12x + x2 = 23 + -23 Combine like terms: 36 + -23 = 13 13 + 12x + x2 = 23 + -23 Combine like terms: 23 + -23 = 0 13 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 12x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 12x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 12x + x2 = 0 + -13 12x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 12x + x2 = -13 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 = -13 + 36 Reorder the terms: 36 + 12x + x2 = -13 + 36 Combine like terms: -13 + 36 = 23 36 + 12x + x2 = 23 Factor a perfect square on the left side: (x + 6)(x + 6) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 6) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 6 = 4.795831523 Simplifying x + 6 = 4.795831523 Reorder the terms: 6 + x = 4.795831523 Solving 6 + x = 4.795831523 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 = 4.795831523 + -6 Combine like terms: 6 + -6 = 0 0 + x = 4.795831523 + -6 x = 4.795831523 + -6 Combine like terms: 4.795831523 + -6 = -1.204168477 x = -1.204168477 Simplifying x = -1.204168477Subproblem 2
x + 6 = -4.795831523 Simplifying x + 6 = -4.795831523 Reorder the terms: 6 + x = -4.795831523 Solving 6 + x = -4.795831523 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 = -4.795831523 + -6 Combine like terms: 6 + -6 = 0 0 + x = -4.795831523 + -6 x = -4.795831523 + -6 Combine like terms: -4.795831523 + -6 = -10.795831523 x = -10.795831523 Simplifying x = -10.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.204168477, -10.795831523}
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