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Simplifying x2 + -37x + 27 = 0 Reorder the terms: 27 + -37x + x2 = 0 Solving 27 + -37x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -37x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -37x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -37x + x2 = 0 + -27 -37x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -37x + x2 = -27 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 = -27 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -27 + 342.25 Combine like terms: -27 + 342.25 = 315.25 342.25 + -37x + x2 = 315.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 315.25 Calculate the square root of the right side: 17.755280905 Break this problem into two subproblems by setting (x + -18.5) equal to 17.755280905 and -17.755280905.Subproblem 1
x + -18.5 = 17.755280905 Simplifying x + -18.5 = 17.755280905 Reorder the terms: -18.5 + x = 17.755280905 Solving -18.5 + x = 17.755280905 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 = 17.755280905 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 17.755280905 + 18.5 x = 17.755280905 + 18.5 Combine like terms: 17.755280905 + 18.5 = 36.255280905 x = 36.255280905 Simplifying x = 36.255280905Subproblem 2
x + -18.5 = -17.755280905 Simplifying x + -18.5 = -17.755280905 Reorder the terms: -18.5 + x = -17.755280905 Solving -18.5 + x = -17.755280905 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 = -17.755280905 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -17.755280905 + 18.5 x = -17.755280905 + 18.5 Combine like terms: -17.755280905 + 18.5 = 0.744719095 x = 0.744719095 Simplifying x = 0.744719095Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.255280905, 0.744719095}
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