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Simplifying (x + -1)(x + 12) = 7 Reorder the terms: (-1 + x)(x + 12) = 7 Reorder the terms: (-1 + x)(12 + x) = 7 Multiply (-1 + x) * (12 + x) (-1(12 + x) + x(12 + x)) = 7 ((12 * -1 + x * -1) + x(12 + x)) = 7 ((-12 + -1x) + x(12 + x)) = 7 (-12 + -1x + (12 * x + x * x)) = 7 (-12 + -1x + (12x + x2)) = 7 Combine like terms: -1x + 12x = 11x (-12 + 11x + x2) = 7 Solving -12 + 11x + x2 = 7 Solving for variable 'x'. Reorder the terms: -12 + -7 + 11x + x2 = 7 + -7 Combine like terms: -12 + -7 = -19 -19 + 11x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -19 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 11x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 11x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 11x + x2 = 0 + 19 11x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 11x + x2 = 19 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 19 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 19 + 30.25 Combine like terms: 19 + 30.25 = 49.25 30.25 + 11x + x2 = 49.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (x + 5.5) equal to 7.017834424 and -7.017834424.Subproblem 1
x + 5.5 = 7.017834424 Simplifying x + 5.5 = 7.017834424 Reorder the terms: 5.5 + x = 7.017834424 Solving 5.5 + x = 7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 7.017834424 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.017834424 + -5.5 x = 7.017834424 + -5.5 Combine like terms: 7.017834424 + -5.5 = 1.517834424 x = 1.517834424 Simplifying x = 1.517834424Subproblem 2
x + 5.5 = -7.017834424 Simplifying x + 5.5 = -7.017834424 Reorder the terms: 5.5 + x = -7.017834424 Solving 5.5 + x = -7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -7.017834424 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.017834424 + -5.5 x = -7.017834424 + -5.5 Combine like terms: -7.017834424 + -5.5 = -12.517834424 x = -12.517834424 Simplifying x = -12.517834424Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.517834424, -12.517834424}
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