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Simplifying (x + 19)(x + 5) = -2 Reorder the terms: (19 + x)(x + 5) = -2 Reorder the terms: (19 + x)(5 + x) = -2 Multiply (19 + x) * (5 + x) (19(5 + x) + x(5 + x)) = -2 ((5 * 19 + x * 19) + x(5 + x)) = -2 ((95 + 19x) + x(5 + x)) = -2 (95 + 19x + (5 * x + x * x)) = -2 (95 + 19x + (5x + x2)) = -2 Combine like terms: 19x + 5x = 24x (95 + 24x + x2) = -2 Solving 95 + 24x + x2 = -2 Solving for variable 'x'. Reorder the terms: 95 + 2 + 24x + x2 = -2 + 2 Combine like terms: 95 + 2 = 97 97 + 24x + x2 = -2 + 2 Combine like terms: -2 + 2 = 0 97 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-97' to each side of the equation. 97 + 24x + -97 + x2 = 0 + -97 Reorder the terms: 97 + -97 + 24x + x2 = 0 + -97 Combine like terms: 97 + -97 = 0 0 + 24x + x2 = 0 + -97 24x + x2 = 0 + -97 Combine like terms: 0 + -97 = -97 24x + x2 = -97 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 = -97 + 144 Reorder the terms: 144 + 24x + x2 = -97 + 144 Combine like terms: -97 + 144 = 47 144 + 24x + x2 = 47 Factor a perfect square on the left side: (x + 12)(x + 12) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + 12) equal to 6.8556546 and -6.8556546.Subproblem 1
x + 12 = 6.8556546 Simplifying x + 12 = 6.8556546 Reorder the terms: 12 + x = 6.8556546 Solving 12 + x = 6.8556546 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 = 6.8556546 + -12 Combine like terms: 12 + -12 = 0 0 + x = 6.8556546 + -12 x = 6.8556546 + -12 Combine like terms: 6.8556546 + -12 = -5.1443454 x = -5.1443454 Simplifying x = -5.1443454Subproblem 2
x + 12 = -6.8556546 Simplifying x + 12 = -6.8556546 Reorder the terms: 12 + x = -6.8556546 Solving 12 + x = -6.8556546 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 = -6.8556546 + -12 Combine like terms: 12 + -12 = 0 0 + x = -6.8556546 + -12 x = -6.8556546 + -12 Combine like terms: -6.8556546 + -12 = -18.8556546 x = -18.8556546 Simplifying x = -18.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.1443454, -18.8556546}
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