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Simplifying x2 + 16x + -82 = 0 Reorder the terms: -82 + 16x + x2 = 0 Solving -82 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + 16x + 82 + x2 = 0 + 82 Reorder the terms: -82 + 82 + 16x + x2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + 16x + x2 = 0 + 82 16x + x2 = 0 + 82 Combine like terms: 0 + 82 = 82 16x + x2 = 82 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 = 82 + 64 Reorder the terms: 64 + 16x + x2 = 82 + 64 Combine like terms: 82 + 64 = 146 64 + 16x + x2 = 146 Factor a perfect square on the left side: (x + 8)(x + 8) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (x + 8) equal to 12.083045974 and -12.083045974.Subproblem 1
x + 8 = 12.083045974 Simplifying x + 8 = 12.083045974 Reorder the terms: 8 + x = 12.083045974 Solving 8 + x = 12.083045974 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 = 12.083045974 + -8 Combine like terms: 8 + -8 = 0 0 + x = 12.083045974 + -8 x = 12.083045974 + -8 Combine like terms: 12.083045974 + -8 = 4.083045974 x = 4.083045974 Simplifying x = 4.083045974Subproblem 2
x + 8 = -12.083045974 Simplifying x + 8 = -12.083045974 Reorder the terms: 8 + x = -12.083045974 Solving 8 + x = -12.083045974 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 = -12.083045974 + -8 Combine like terms: 8 + -8 = 0 0 + x = -12.083045974 + -8 x = -12.083045974 + -8 Combine like terms: -12.083045974 + -8 = -20.083045974 x = -20.083045974 Simplifying x = -20.083045974Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.083045974, -20.083045974}
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