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Simplifying x2 + -120x + 30 = 0 Reorder the terms: 30 + -120x + x2 = 0 Solving 30 + -120x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -120x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -120x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -120x + x2 = 0 + -30 -120x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -120x + x2 = -30 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 = -30 + 3600 Reorder the terms: 3600 + -120x + x2 = -30 + 3600 Combine like terms: -30 + 3600 = 3570 3600 + -120x + x2 = 3570 Factor a perfect square on the left side: (x + -60)(x + -60) = 3570 Calculate the square root of the right side: 59.749476985 Break this problem into two subproblems by setting (x + -60) equal to 59.749476985 and -59.749476985.Subproblem 1
x + -60 = 59.749476985 Simplifying x + -60 = 59.749476985 Reorder the terms: -60 + x = 59.749476985 Solving -60 + x = 59.749476985 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 = 59.749476985 + 60 Combine like terms: -60 + 60 = 0 0 + x = 59.749476985 + 60 x = 59.749476985 + 60 Combine like terms: 59.749476985 + 60 = 119.749476985 x = 119.749476985 Simplifying x = 119.749476985Subproblem 2
x + -60 = -59.749476985 Simplifying x + -60 = -59.749476985 Reorder the terms: -60 + x = -59.749476985 Solving -60 + x = -59.749476985 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 = -59.749476985 + 60 Combine like terms: -60 + 60 = 0 0 + x = -59.749476985 + 60 x = -59.749476985 + 60 Combine like terms: -59.749476985 + 60 = 0.250523015 x = 0.250523015 Simplifying x = 0.250523015Solution
The solution to the problem is based on the solutions from the subproblems. x = {119.749476985, 0.250523015}
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