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Simplifying (x + -2)(x + 12) = 12 Reorder the terms: (-2 + x)(x + 12) = 12 Reorder the terms: (-2 + x)(12 + x) = 12 Multiply (-2 + x) * (12 + x) (-2(12 + x) + x(12 + x)) = 12 ((12 * -2 + x * -2) + x(12 + x)) = 12 ((-24 + -2x) + x(12 + x)) = 12 (-24 + -2x + (12 * x + x * x)) = 12 (-24 + -2x + (12x + x2)) = 12 Combine like terms: -2x + 12x = 10x (-24 + 10x + x2) = 12 Solving -24 + 10x + x2 = 12 Solving for variable 'x'. Reorder the terms: -24 + -12 + 10x + x2 = 12 + -12 Combine like terms: -24 + -12 = -36 -36 + 10x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -36 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 10x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 10x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 10x + x2 = 0 + 36 10x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 10x + x2 = 36 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 36 + 25 Reorder the terms: 25 + 10x + x2 = 36 + 25 Combine like terms: 36 + 25 = 61 25 + 10x + x2 = 61 Factor a perfect square on the left side: (x + 5)(x + 5) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + 5) equal to 7.810249676 and -7.810249676.Subproblem 1
x + 5 = 7.810249676 Simplifying x + 5 = 7.810249676 Reorder the terms: 5 + x = 7.810249676 Solving 5 + x = 7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 7.810249676 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.810249676 + -5 x = 7.810249676 + -5 Combine like terms: 7.810249676 + -5 = 2.810249676 x = 2.810249676 Simplifying x = 2.810249676Subproblem 2
x + 5 = -7.810249676 Simplifying x + 5 = -7.810249676 Reorder the terms: 5 + x = -7.810249676 Solving 5 + x = -7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -7.810249676 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.810249676 + -5 x = -7.810249676 + -5 Combine like terms: -7.810249676 + -5 = -12.810249676 x = -12.810249676 Simplifying x = -12.810249676Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.810249676, -12.810249676}
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