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Simplifying (x + 17)(x + 7) = -3 Reorder the terms: (17 + x)(x + 7) = -3 Reorder the terms: (17 + x)(7 + x) = -3 Multiply (17 + x) * (7 + x) (17(7 + x) + x(7 + x)) = -3 ((7 * 17 + x * 17) + x(7 + x)) = -3 ((119 + 17x) + x(7 + x)) = -3 (119 + 17x + (7 * x + x * x)) = -3 (119 + 17x + (7x + x2)) = -3 Combine like terms: 17x + 7x = 24x (119 + 24x + x2) = -3 Solving 119 + 24x + x2 = -3 Solving for variable 'x'. Reorder the terms: 119 + 3 + 24x + x2 = -3 + 3 Combine like terms: 119 + 3 = 122 122 + 24x + x2 = -3 + 3 Combine like terms: -3 + 3 = 0 122 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-122' to each side of the equation. 122 + 24x + -122 + x2 = 0 + -122 Reorder the terms: 122 + -122 + 24x + x2 = 0 + -122 Combine like terms: 122 + -122 = 0 0 + 24x + x2 = 0 + -122 24x + x2 = 0 + -122 Combine like terms: 0 + -122 = -122 24x + x2 = -122 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = -122 + 144 Reorder the terms: 144 + 24x + x2 = -122 + 144 Combine like terms: -122 + 144 = 22 144 + 24x + x2 = 22 Factor a perfect square on the left side: (x + 12)(x + 12) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + 12) equal to 4.69041576 and -4.69041576.Subproblem 1
x + 12 = 4.69041576 Simplifying x + 12 = 4.69041576 Reorder the terms: 12 + x = 4.69041576 Solving 12 + x = 4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 4.69041576 + -12 Combine like terms: 12 + -12 = 0 0 + x = 4.69041576 + -12 x = 4.69041576 + -12 Combine like terms: 4.69041576 + -12 = -7.30958424 x = -7.30958424 Simplifying x = -7.30958424Subproblem 2
x + 12 = -4.69041576 Simplifying x + 12 = -4.69041576 Reorder the terms: 12 + x = -4.69041576 Solving 12 + x = -4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -4.69041576 + -12 Combine like terms: 12 + -12 = 0 0 + x = -4.69041576 + -12 x = -4.69041576 + -12 Combine like terms: -4.69041576 + -12 = -16.69041576 x = -16.69041576 Simplifying x = -16.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.30958424, -16.69041576}
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