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Simplifying x2 + 120x + -45 = 0 Reorder the terms: -45 + 120x + x2 = 0 Solving -45 + 120x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 120x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 120x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 120x + x2 = 0 + 45 120x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 120x + x2 = 45 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 = 45 + 3600 Reorder the terms: 3600 + 120x + x2 = 45 + 3600 Combine like terms: 45 + 3600 = 3645 3600 + 120x + x2 = 3645 Factor a perfect square on the left side: (x + 60)(x + 60) = 3645 Calculate the square root of the right side: 60.373835392 Break this problem into two subproblems by setting (x + 60) equal to 60.373835392 and -60.373835392.Subproblem 1
x + 60 = 60.373835392 Simplifying x + 60 = 60.373835392 Reorder the terms: 60 + x = 60.373835392 Solving 60 + x = 60.373835392 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 = 60.373835392 + -60 Combine like terms: 60 + -60 = 0 0 + x = 60.373835392 + -60 x = 60.373835392 + -60 Combine like terms: 60.373835392 + -60 = 0.373835392 x = 0.373835392 Simplifying x = 0.373835392Subproblem 2
x + 60 = -60.373835392 Simplifying x + 60 = -60.373835392 Reorder the terms: 60 + x = -60.373835392 Solving 60 + x = -60.373835392 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 = -60.373835392 + -60 Combine like terms: 60 + -60 = 0 0 + x = -60.373835392 + -60 x = -60.373835392 + -60 Combine like terms: -60.373835392 + -60 = -120.373835392 x = -120.373835392 Simplifying x = -120.373835392Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.373835392, -120.373835392}
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