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Simplifying x2 + 81x + 62 = 0 Reorder the terms: 62 + 81x + x2 = 0 Solving 62 + 81x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-62' to each side of the equation. 62 + 81x + -62 + x2 = 0 + -62 Reorder the terms: 62 + -62 + 81x + x2 = 0 + -62 Combine like terms: 62 + -62 = 0 0 + 81x + x2 = 0 + -62 81x + x2 = 0 + -62 Combine like terms: 0 + -62 = -62 81x + x2 = -62 The x term is 81x. Take half its coefficient (40.5). Square it (1640.25) and add it to both sides. Add '1640.25' to each side of the equation. 81x + 1640.25 + x2 = -62 + 1640.25 Reorder the terms: 1640.25 + 81x + x2 = -62 + 1640.25 Combine like terms: -62 + 1640.25 = 1578.25 1640.25 + 81x + x2 = 1578.25 Factor a perfect square on the left side: (x + 40.5)(x + 40.5) = 1578.25 Calculate the square root of the right side: 39.727194716 Break this problem into two subproblems by setting (x + 40.5) equal to 39.727194716 and -39.727194716.Subproblem 1
x + 40.5 = 39.727194716 Simplifying x + 40.5 = 39.727194716 Reorder the terms: 40.5 + x = 39.727194716 Solving 40.5 + x = 39.727194716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + x = 39.727194716 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = 39.727194716 + -40.5 x = 39.727194716 + -40.5 Combine like terms: 39.727194716 + -40.5 = -0.772805284 x = -0.772805284 Simplifying x = -0.772805284Subproblem 2
x + 40.5 = -39.727194716 Simplifying x + 40.5 = -39.727194716 Reorder the terms: 40.5 + x = -39.727194716 Solving 40.5 + x = -39.727194716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + x = -39.727194716 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = -39.727194716 + -40.5 x = -39.727194716 + -40.5 Combine like terms: -39.727194716 + -40.5 = -80.227194716 x = -80.227194716 Simplifying x = -80.227194716Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.772805284, -80.227194716}
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