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Simplifying x2 + 120x + 10 = 0 Reorder the terms: 10 + 120x + x2 = 0 Solving 10 + 120x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 120x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 120x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 120x + x2 = 0 + -10 120x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 120x + x2 = -10 The x term is 120x. Take half its coefficient (60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. 120x + 3600 + x2 = -10 + 3600 Reorder the terms: 3600 + 120x + x2 = -10 + 3600 Combine like terms: -10 + 3600 = 3590 3600 + 120x + x2 = 3590 Factor a perfect square on the left side: (x + 60)(x + 60) = 3590 Calculate the square root of the right side: 59.916608716 Break this problem into two subproblems by setting (x + 60) equal to 59.916608716 and -59.916608716.Subproblem 1
x + 60 = 59.916608716 Simplifying x + 60 = 59.916608716 Reorder the terms: 60 + x = 59.916608716 Solving 60 + x = 59.916608716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + x = 59.916608716 + -60 Combine like terms: 60 + -60 = 0 0 + x = 59.916608716 + -60 x = 59.916608716 + -60 Combine like terms: 59.916608716 + -60 = -0.083391284 x = -0.083391284 Simplifying x = -0.083391284Subproblem 2
x + 60 = -59.916608716 Simplifying x + 60 = -59.916608716 Reorder the terms: 60 + x = -59.916608716 Solving 60 + x = -59.916608716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + x = -59.916608716 + -60 Combine like terms: 60 + -60 = 0 0 + x = -59.916608716 + -60 x = -59.916608716 + -60 Combine like terms: -59.916608716 + -60 = -119.916608716 x = -119.916608716 Simplifying x = -119.916608716Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.083391284, -119.916608716}
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