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Simplifying X2 + 2X + -192 = 0 Reorder the terms: -192 + 2X + X2 = 0 Solving -192 + 2X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + 2X + 192 + X2 = 0 + 192 Reorder the terms: -192 + 192 + 2X + X2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 2X + X2 = 0 + 192 2X + X2 = 0 + 192 Combine like terms: 0 + 192 = 192 2X + X2 = 192 The X term is 2X. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2X + 1 + X2 = 192 + 1 Reorder the terms: 1 + 2X + X2 = 192 + 1 Combine like terms: 192 + 1 = 193 1 + 2X + X2 = 193 Factor a perfect square on the left side: (X + 1)(X + 1) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (X + 1) equal to 13.892443989 and -13.892443989.Subproblem 1
X + 1 = 13.892443989 Simplifying X + 1 = 13.892443989 Reorder the terms: 1 + X = 13.892443989 Solving 1 + X = 13.892443989 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = 13.892443989 + -1 Combine like terms: 1 + -1 = 0 0 + X = 13.892443989 + -1 X = 13.892443989 + -1 Combine like terms: 13.892443989 + -1 = 12.892443989 X = 12.892443989 Simplifying X = 12.892443989Subproblem 2
X + 1 = -13.892443989 Simplifying X + 1 = -13.892443989 Reorder the terms: 1 + X = -13.892443989 Solving 1 + X = -13.892443989 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = -13.892443989 + -1 Combine like terms: 1 + -1 = 0 0 + X = -13.892443989 + -1 X = -13.892443989 + -1 Combine like terms: -13.892443989 + -1 = -14.892443989 X = -14.892443989 Simplifying X = -14.892443989Solution
The solution to the problem is based on the solutions from the subproblems. X = {12.892443989, -14.892443989}
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