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Simplifying (x + 12)(x + 10) = 2 Reorder the terms: (12 + x)(x + 10) = 2 Reorder the terms: (12 + x)(10 + x) = 2 Multiply (12 + x) * (10 + x) (12(10 + x) + x(10 + x)) = 2 ((10 * 12 + x * 12) + x(10 + x)) = 2 ((120 + 12x) + x(10 + x)) = 2 (120 + 12x + (10 * x + x * x)) = 2 (120 + 12x + (10x + x2)) = 2 Combine like terms: 12x + 10x = 22x (120 + 22x + x2) = 2 Solving 120 + 22x + x2 = 2 Solving for variable 'x'. Reorder the terms: 120 + -2 + 22x + x2 = 2 + -2 Combine like terms: 120 + -2 = 118 118 + 22x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 118 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-118' to each side of the equation. 118 + 22x + -118 + x2 = 0 + -118 Reorder the terms: 118 + -118 + 22x + x2 = 0 + -118 Combine like terms: 118 + -118 = 0 0 + 22x + x2 = 0 + -118 22x + x2 = 0 + -118 Combine like terms: 0 + -118 = -118 22x + x2 = -118 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = -118 + 121 Reorder the terms: 121 + 22x + x2 = -118 + 121 Combine like terms: -118 + 121 = 3 121 + 22x + x2 = 3 Factor a perfect square on the left side: (x + 11)(x + 11) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 11) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 11 = 1.732050808 Simplifying x + 11 = 1.732050808 Reorder the terms: 11 + x = 1.732050808 Solving 11 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 1.732050808 + -11 Combine like terms: 11 + -11 = 0 0 + x = 1.732050808 + -11 x = 1.732050808 + -11 Combine like terms: 1.732050808 + -11 = -9.267949192 x = -9.267949192 Simplifying x = -9.267949192Subproblem 2
x + 11 = -1.732050808 Simplifying x + 11 = -1.732050808 Reorder the terms: 11 + x = -1.732050808 Solving 11 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -1.732050808 + -11 Combine like terms: 11 + -11 = 0 0 + x = -1.732050808 + -11 x = -1.732050808 + -11 Combine like terms: -1.732050808 + -11 = -12.732050808 x = -12.732050808 Simplifying x = -12.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-9.267949192, -12.732050808}
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