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Simplifying x2 + -120x + -144 = 0 Reorder the terms: -144 + -120x + x2 = 0 Solving -144 + -120x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -120x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -120x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -120x + x2 = 0 + 144 -120x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -120x + x2 = 144 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 = 144 + 3600 Reorder the terms: 3600 + -120x + x2 = 144 + 3600 Combine like terms: 144 + 3600 = 3744 3600 + -120x + x2 = 3744 Factor a perfect square on the left side: (x + -60)(x + -60) = 3744 Calculate the square root of the right side: 61.188234163 Break this problem into two subproblems by setting (x + -60) equal to 61.188234163 and -61.188234163.Subproblem 1
x + -60 = 61.188234163 Simplifying x + -60 = 61.188234163 Reorder the terms: -60 + x = 61.188234163 Solving -60 + x = 61.188234163 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 = 61.188234163 + 60 Combine like terms: -60 + 60 = 0 0 + x = 61.188234163 + 60 x = 61.188234163 + 60 Combine like terms: 61.188234163 + 60 = 121.188234163 x = 121.188234163 Simplifying x = 121.188234163Subproblem 2
x + -60 = -61.188234163 Simplifying x + -60 = -61.188234163 Reorder the terms: -60 + x = -61.188234163 Solving -60 + x = -61.188234163 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 = -61.188234163 + 60 Combine like terms: -60 + 60 = 0 0 + x = -61.188234163 + 60 x = -61.188234163 + 60 Combine like terms: -61.188234163 + 60 = -1.188234163 x = -1.188234163 Simplifying x = -1.188234163Solution
The solution to the problem is based on the solutions from the subproblems. x = {121.188234163, -1.188234163}
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