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Simplifying X2 + -31X + 60 = 0 Reorder the terms: 60 + -31X + X2 = 0 Solving 60 + -31X + 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 + -31X + -60 + X2 = 0 + -60 Reorder the terms: 60 + -60 + -31X + X2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -31X + X2 = 0 + -60 -31X + X2 = 0 + -60 Combine like terms: 0 + -60 = -60 -31X + X2 = -60 The X term is -31X. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31X + 240.25 + X2 = -60 + 240.25 Reorder the terms: 240.25 + -31X + X2 = -60 + 240.25 Combine like terms: -60 + 240.25 = 180.25 240.25 + -31X + X2 = 180.25 Factor a perfect square on the left side: (X + -15.5)(X + -15.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (X + -15.5) equal to 13.425721582 and -13.425721582.Subproblem 1
X + -15.5 = 13.425721582 Simplifying X + -15.5 = 13.425721582 Reorder the terms: -15.5 + X = 13.425721582 Solving -15.5 + X = 13.425721582 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + X = 13.425721582 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + X = 13.425721582 + 15.5 X = 13.425721582 + 15.5 Combine like terms: 13.425721582 + 15.5 = 28.925721582 X = 28.925721582 Simplifying X = 28.925721582Subproblem 2
X + -15.5 = -13.425721582 Simplifying X + -15.5 = -13.425721582 Reorder the terms: -15.5 + X = -13.425721582 Solving -15.5 + X = -13.425721582 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + X = -13.425721582 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + X = -13.425721582 + 15.5 X = -13.425721582 + 15.5 Combine like terms: -13.425721582 + 15.5 = 2.074278418 X = 2.074278418 Simplifying X = 2.074278418Solution
The solution to the problem is based on the solutions from the subproblems. X = {28.925721582, 2.074278418}
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