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Simplifying x2 + 16x + -92 = 0 Reorder the terms: -92 + 16x + x2 = 0 Solving -92 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + 16x + 92 + x2 = 0 + 92 Reorder the terms: -92 + 92 + 16x + x2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + 16x + x2 = 0 + 92 16x + x2 = 0 + 92 Combine like terms: 0 + 92 = 92 16x + x2 = 92 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 92 + 64 Reorder the terms: 64 + 16x + x2 = 92 + 64 Combine like terms: 92 + 64 = 156 64 + 16x + x2 = 156 Factor a perfect square on the left side: (x + 8)(x + 8) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (x + 8) equal to 12.489995997 and -12.489995997.Subproblem 1
x + 8 = 12.489995997 Simplifying x + 8 = 12.489995997 Reorder the terms: 8 + x = 12.489995997 Solving 8 + x = 12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 12.489995997 + -8 Combine like terms: 8 + -8 = 0 0 + x = 12.489995997 + -8 x = 12.489995997 + -8 Combine like terms: 12.489995997 + -8 = 4.489995997 x = 4.489995997 Simplifying x = 4.489995997Subproblem 2
x + 8 = -12.489995997 Simplifying x + 8 = -12.489995997 Reorder the terms: 8 + x = -12.489995997 Solving 8 + x = -12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -12.489995997 + -8 Combine like terms: 8 + -8 = 0 0 + x = -12.489995997 + -8 x = -12.489995997 + -8 Combine like terms: -12.489995997 + -8 = -20.489995997 x = -20.489995997 Simplifying x = -20.489995997Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.489995997, -20.489995997}
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