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Simplifying X2 + -1X + -60 = 0 Reorder the terms: -60 + -1X + X2 = 0 Solving -60 + -1X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -1X + 60 + X2 = 0 + 60 Reorder the terms: -60 + 60 + -1X + X2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -1X + X2 = 0 + 60 -1X + X2 = 0 + 60 Combine like terms: 0 + 60 = 60 -1X + X2 = 60 The X term is -1X. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1X + 0.25 + X2 = 60 + 0.25 Reorder the terms: 0.25 + -1X + X2 = 60 + 0.25 Combine like terms: 60 + 0.25 = 60.25 0.25 + -1X + X2 = 60.25 Factor a perfect square on the left side: (X + -0.5)(X + -0.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (X + -0.5) equal to 7.762087348 and -7.762087348.Subproblem 1
X + -0.5 = 7.762087348 Simplifying X + -0.5 = 7.762087348 Reorder the terms: -0.5 + X = 7.762087348 Solving -0.5 + X = 7.762087348 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = 7.762087348 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 7.762087348 + 0.5 X = 7.762087348 + 0.5 Combine like terms: 7.762087348 + 0.5 = 8.262087348 X = 8.262087348 Simplifying X = 8.262087348Subproblem 2
X + -0.5 = -7.762087348 Simplifying X + -0.5 = -7.762087348 Reorder the terms: -0.5 + X = -7.762087348 Solving -0.5 + X = -7.762087348 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = -7.762087348 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -7.762087348 + 0.5 X = -7.762087348 + 0.5 Combine like terms: -7.762087348 + 0.5 = -7.262087348 X = -7.262087348 Simplifying X = -7.262087348Solution
The solution to the problem is based on the solutions from the subproblems. X = {8.262087348, -7.262087348}
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