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Simplifying [(x + 6)(x + 6)] + 2 = 23 Reorder the terms: [(6 + x)(x + 6)] + 2 = 23 Reorder the terms: [(6 + x)(6 + x)] + 2 = 23 Multiply (6 + x) * (6 + x) [(6(6 + x) + x(6 + x))] + 2 = 23 [((6 * 6 + x * 6) + x(6 + x))] + 2 = 23 [((36 + 6x) + x(6 + x))] + 2 = 23 [(36 + 6x + (6 * x + x * x))] + 2 = 23 [(36 + 6x + (6x + x2))] + 2 = 23 Combine like terms: 6x + 6x = 12x [(36 + 12x + x2)] + 2 = 23 [36 + 12x + x2] + 2 = 23 Remove brackets around [36 + 12x + x2] 36 + 12x + x2 + 2 = 23 Reorder the terms: 36 + 2 + 12x + x2 = 23 Combine like terms: 36 + 2 = 38 38 + 12x + x2 = 23 Solving 38 + 12x + x2 = 23 Solving for variable 'x'. Reorder the terms: 38 + -23 + 12x + x2 = 23 + -23 Combine like terms: 38 + -23 = 15 15 + 12x + x2 = 23 + -23 Combine like terms: 23 + -23 = 0 15 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 12x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 12x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 12x + x2 = 0 + -15 12x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 12x + x2 = -15 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 = -15 + 36 Reorder the terms: 36 + 12x + x2 = -15 + 36 Combine like terms: -15 + 36 = 21 36 + 12x + x2 = 21 Factor a perfect square on the left side: (x + 6)(x + 6) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + 6) equal to 4.582575695 and -4.582575695.Subproblem 1
x + 6 = 4.582575695 Simplifying x + 6 = 4.582575695 Reorder the terms: 6 + x = 4.582575695 Solving 6 + x = 4.582575695 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 = 4.582575695 + -6 Combine like terms: 6 + -6 = 0 0 + x = 4.582575695 + -6 x = 4.582575695 + -6 Combine like terms: 4.582575695 + -6 = -1.417424305 x = -1.417424305 Simplifying x = -1.417424305Subproblem 2
x + 6 = -4.582575695 Simplifying x + 6 = -4.582575695 Reorder the terms: 6 + x = -4.582575695 Solving 6 + x = -4.582575695 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 = -4.582575695 + -6 Combine like terms: 6 + -6 = 0 0 + x = -4.582575695 + -6 x = -4.582575695 + -6 Combine like terms: -4.582575695 + -6 = -10.582575695 x = -10.582575695 Simplifying x = -10.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.417424305, -10.582575695}
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