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Simplifying 192 = (x + 2)(x + 4) Reorder the terms: 192 = (2 + x)(x + 4) Reorder the terms: 192 = (2 + x)(4 + x) Multiply (2 + x) * (4 + x) 192 = (2(4 + x) + x(4 + x)) 192 = ((4 * 2 + x * 2) + x(4 + x)) 192 = ((8 + 2x) + x(4 + x)) 192 = (8 + 2x + (4 * x + x * x)) 192 = (8 + 2x + (4x + x2)) Combine like terms: 2x + 4x = 6x 192 = (8 + 6x + x2) Solving 192 = 8 + 6x + x2 Solving for variable 'x'. Combine like terms: 192 + -8 = 184 184 + -6x + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2 Reorder the terms: 184 + -6x + -1x2 = 8 + -8 + 6x + -6x + x2 + -1x2 Combine like terms: 8 + -8 = 0 184 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 184 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 184 + -6x + -1x2 = 0 + x2 + -1x2 184 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 184 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -184 + 6x + x2 = 0 Move the constant term to the right: Add '184' to each side of the equation. -184 + 6x + 184 + x2 = 0 + 184 Reorder the terms: -184 + 184 + 6x + x2 = 0 + 184 Combine like terms: -184 + 184 = 0 0 + 6x + x2 = 0 + 184 6x + x2 = 0 + 184 Combine like terms: 0 + 184 = 184 6x + x2 = 184 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 184 + 9 Reorder the terms: 9 + 6x + x2 = 184 + 9 Combine like terms: 184 + 9 = 193 9 + 6x + x2 = 193 Factor a perfect square on the left side: (x + 3)(x + 3) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (x + 3) equal to 13.892443989 and -13.892443989.Subproblem 1
x + 3 = 13.892443989 Simplifying x + 3 = 13.892443989 Reorder the terms: 3 + x = 13.892443989 Solving 3 + x = 13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 13.892443989 + -3 Combine like terms: 3 + -3 = 0 0 + x = 13.892443989 + -3 x = 13.892443989 + -3 Combine like terms: 13.892443989 + -3 = 10.892443989 x = 10.892443989 Simplifying x = 10.892443989Subproblem 2
x + 3 = -13.892443989 Simplifying x + 3 = -13.892443989 Reorder the terms: 3 + x = -13.892443989 Solving 3 + x = -13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -13.892443989 + -3 Combine like terms: 3 + -3 = 0 0 + x = -13.892443989 + -3 x = -13.892443989 + -3 Combine like terms: -13.892443989 + -3 = -16.892443989 x = -16.892443989 Simplifying x = -16.892443989Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.892443989, -16.892443989}
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