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Simplifying 2(x2 + 2x + -192) = 0 Reorder the terms: 2(-192 + 2x + x2) = 0 (-192 * 2 + 2x * 2 + x2 * 2) = 0 (-384 + 4x + 2x2) = 0 Solving -384 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-192 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-192 + 2x + x2)' equal to zero and attempt to solve: Simplifying -192 + 2x + x2 = 0 Solving -192 + 2x + x2 = 0 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}Solution
x = {12.892443989, -14.892443989}
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