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Simplifying (x)(12 + x) = 120 (12 * x + x * x) = 120 (12x + x2) = 120 Solving 12x + x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 12x + x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 12x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 12x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 12x + x2 = 0 + 120 12x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 12x + x2 = 120 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 = 120 + 36 Reorder the terms: 36 + 12x + x2 = 120 + 36 Combine like terms: 120 + 36 = 156 36 + 12x + x2 = 156 Factor a perfect square on the left side: (x + 6)(x + 6) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (x + 6) equal to 12.489995997 and -12.489995997.Subproblem 1
x + 6 = 12.489995997 Simplifying x + 6 = 12.489995997 Reorder the terms: 6 + x = 12.489995997 Solving 6 + x = 12.489995997 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 = 12.489995997 + -6 Combine like terms: 6 + -6 = 0 0 + x = 12.489995997 + -6 x = 12.489995997 + -6 Combine like terms: 12.489995997 + -6 = 6.489995997 x = 6.489995997 Simplifying x = 6.489995997Subproblem 2
x + 6 = -12.489995997 Simplifying x + 6 = -12.489995997 Reorder the terms: 6 + x = -12.489995997 Solving 6 + x = -12.489995997 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 = -12.489995997 + -6 Combine like terms: 6 + -6 = 0 0 + x = -12.489995997 + -6 x = -12.489995997 + -6 Combine like terms: -12.489995997 + -6 = -18.489995997 x = -18.489995997 Simplifying x = -18.489995997Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.489995997, -18.489995997}
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