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Simplifying (x + 6)(x + 6) + -28 = 0 Reorder the terms: (6 + x)(x + 6) + -28 = 0 Reorder the terms: (6 + x)(6 + x) + -28 = 0 Multiply (6 + x) * (6 + x) (6(6 + x) + x(6 + x)) + -28 = 0 ((6 * 6 + x * 6) + x(6 + x)) + -28 = 0 ((36 + 6x) + x(6 + x)) + -28 = 0 (36 + 6x + (6 * x + x * x)) + -28 = 0 (36 + 6x + (6x + x2)) + -28 = 0 Combine like terms: 6x + 6x = 12x (36 + 12x + x2) + -28 = 0 Reorder the terms: 36 + -28 + 12x + x2 = 0 Combine like terms: 36 + -28 = 8 8 + 12x + x2 = 0 Solving 8 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 12x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 12x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 12x + x2 = 0 + -8 12x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 12x + x2 = -8 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 = -8 + 36 Reorder the terms: 36 + 12x + x2 = -8 + 36 Combine like terms: -8 + 36 = 28 36 + 12x + x2 = 28 Factor a perfect square on the left side: (x + 6)(x + 6) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + 6) equal to 5.291502622 and -5.291502622.Subproblem 1
x + 6 = 5.291502622 Simplifying x + 6 = 5.291502622 Reorder the terms: 6 + x = 5.291502622 Solving 6 + x = 5.291502622 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 = 5.291502622 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.291502622 + -6 x = 5.291502622 + -6 Combine like terms: 5.291502622 + -6 = -0.708497378 x = -0.708497378 Simplifying x = -0.708497378Subproblem 2
x + 6 = -5.291502622 Simplifying x + 6 = -5.291502622 Reorder the terms: 6 + x = -5.291502622 Solving 6 + x = -5.291502622 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 = -5.291502622 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.291502622 + -6 x = -5.291502622 + -6 Combine like terms: -5.291502622 + -6 = -11.291502622 x = -11.291502622 Simplifying x = -11.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.708497378, -11.291502622}
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