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Simplifying x2 + -60x + 120 = 0 Reorder the terms: 120 + -60x + x2 = 0 Solving 120 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + -60x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + -60x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -60x + x2 = 0 + -120 -60x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 -60x + x2 = -120 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = -120 + 900 Reorder the terms: 900 + -60x + x2 = -120 + 900 Combine like terms: -120 + 900 = 780 900 + -60x + x2 = 780 Factor a perfect square on the left side: (x + -30)(x + -30) = 780 Calculate the square root of the right side: 27.928480088 Break this problem into two subproblems by setting (x + -30) equal to 27.928480088 and -27.928480088.Subproblem 1
x + -30 = 27.928480088 Simplifying x + -30 = 27.928480088 Reorder the terms: -30 + x = 27.928480088 Solving -30 + x = 27.928480088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 27.928480088 + 30 Combine like terms: -30 + 30 = 0 0 + x = 27.928480088 + 30 x = 27.928480088 + 30 Combine like terms: 27.928480088 + 30 = 57.928480088 x = 57.928480088 Simplifying x = 57.928480088Subproblem 2
x + -30 = -27.928480088 Simplifying x + -30 = -27.928480088 Reorder the terms: -30 + x = -27.928480088 Solving -30 + x = -27.928480088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -27.928480088 + 30 Combine like terms: -30 + 30 = 0 0 + x = -27.928480088 + 30 x = -27.928480088 + 30 Combine like terms: -27.928480088 + 30 = 2.071519912 x = 2.071519912 Simplifying x = 2.071519912Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.928480088, 2.071519912}
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