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Simplifying (x + 9)(x + 12) = 1 Reorder the terms: (9 + x)(x + 12) = 1 Reorder the terms: (9 + x)(12 + x) = 1 Multiply (9 + x) * (12 + x) (9(12 + x) + x(12 + x)) = 1 ((12 * 9 + x * 9) + x(12 + x)) = 1 ((108 + 9x) + x(12 + x)) = 1 (108 + 9x + (12 * x + x * x)) = 1 (108 + 9x + (12x + x2)) = 1 Combine like terms: 9x + 12x = 21x (108 + 21x + x2) = 1 Solving 108 + 21x + x2 = 1 Solving for variable 'x'. Reorder the terms: 108 + -1 + 21x + x2 = 1 + -1 Combine like terms: 108 + -1 = 107 107 + 21x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 107 + 21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-107' to each side of the equation. 107 + 21x + -107 + x2 = 0 + -107 Reorder the terms: 107 + -107 + 21x + x2 = 0 + -107 Combine like terms: 107 + -107 = 0 0 + 21x + x2 = 0 + -107 21x + x2 = 0 + -107 Combine like terms: 0 + -107 = -107 21x + x2 = -107 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = -107 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -107 + 110.25 Combine like terms: -107 + 110.25 = 3.25 110.25 + 21x + x2 = 3.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 10.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 10.5 = 1.802775638 Simplifying x + 10.5 = 1.802775638 Reorder the terms: 10.5 + x = 1.802775638 Solving 10.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 1.802775638 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 1.802775638 + -10.5 x = 1.802775638 + -10.5 Combine like terms: 1.802775638 + -10.5 = -8.697224362 x = -8.697224362 Simplifying x = -8.697224362Subproblem 2
x + 10.5 = -1.802775638 Simplifying x + 10.5 = -1.802775638 Reorder the terms: 10.5 + x = -1.802775638 Solving 10.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -1.802775638 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -1.802775638 + -10.5 x = -1.802775638 + -10.5 Combine like terms: -1.802775638 + -10.5 = -12.302775638 x = -12.302775638 Simplifying x = -12.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.697224362, -12.302775638}
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