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Simplifying x2 + -120x + 72 = 0 Reorder the terms: 72 + -120x + x2 = 0 Solving 72 + -120x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + -120x + -72 + x2 = 0 + -72 Reorder the terms: 72 + -72 + -120x + x2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -120x + x2 = 0 + -72 -120x + x2 = 0 + -72 Combine like terms: 0 + -72 = -72 -120x + x2 = -72 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 = -72 + 3600 Reorder the terms: 3600 + -120x + x2 = -72 + 3600 Combine like terms: -72 + 3600 = 3528 3600 + -120x + x2 = 3528 Factor a perfect square on the left side: (x + -60)(x + -60) = 3528 Calculate the square root of the right side: 59.39696962 Break this problem into two subproblems by setting (x + -60) equal to 59.39696962 and -59.39696962.Subproblem 1
x + -60 = 59.39696962 Simplifying x + -60 = 59.39696962 Reorder the terms: -60 + x = 59.39696962 Solving -60 + x = 59.39696962 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 = 59.39696962 + 60 Combine like terms: -60 + 60 = 0 0 + x = 59.39696962 + 60 x = 59.39696962 + 60 Combine like terms: 59.39696962 + 60 = 119.39696962 x = 119.39696962 Simplifying x = 119.39696962Subproblem 2
x + -60 = -59.39696962 Simplifying x + -60 = -59.39696962 Reorder the terms: -60 + x = -59.39696962 Solving -60 + x = -59.39696962 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 = -59.39696962 + 60 Combine like terms: -60 + 60 = 0 0 + x = -59.39696962 + 60 x = -59.39696962 + 60 Combine like terms: -59.39696962 + 60 = 0.60303038 x = 0.60303038 Simplifying x = 0.60303038Solution
The solution to the problem is based on the solutions from the subproblems. x = {119.39696962, 0.60303038}
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