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Simplifying x2 + -37x + -60 = 0 Reorder the terms: -60 + -37x + x2 = 0 Solving -60 + -37x + 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 + -37x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -37x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -37x + x2 = 0 + 60 -37x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -37x + x2 = 60 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = 60 + 342.25 Reorder the terms: 342.25 + -37x + x2 = 60 + 342.25 Combine like terms: 60 + 342.25 = 402.25 342.25 + -37x + x2 = 402.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 402.25 Calculate the square root of the right side: 20.05617112 Break this problem into two subproblems by setting (x + -18.5) equal to 20.05617112 and -20.05617112.Subproblem 1
x + -18.5 = 20.05617112 Simplifying x + -18.5 = 20.05617112 Reorder the terms: -18.5 + x = 20.05617112 Solving -18.5 + x = 20.05617112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 20.05617112 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 20.05617112 + 18.5 x = 20.05617112 + 18.5 Combine like terms: 20.05617112 + 18.5 = 38.55617112 x = 38.55617112 Simplifying x = 38.55617112Subproblem 2
x + -18.5 = -20.05617112 Simplifying x + -18.5 = -20.05617112 Reorder the terms: -18.5 + x = -20.05617112 Solving -18.5 + x = -20.05617112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -20.05617112 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -20.05617112 + 18.5 x = -20.05617112 + 18.5 Combine like terms: -20.05617112 + 18.5 = -1.55617112 x = -1.55617112 Simplifying x = -1.55617112Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.55617112, -1.55617112}
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