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Simplifying x2 + 37x + -1740 = 0 Reorder the terms: -1740 + 37x + x2 = 0 Solving -1740 + 37x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1740' to each side of the equation. -1740 + 37x + 1740 + x2 = 0 + 1740 Reorder the terms: -1740 + 1740 + 37x + x2 = 0 + 1740 Combine like terms: -1740 + 1740 = 0 0 + 37x + x2 = 0 + 1740 37x + x2 = 0 + 1740 Combine like terms: 0 + 1740 = 1740 37x + x2 = 1740 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 = 1740 + 342.25 Reorder the terms: 342.25 + 37x + x2 = 1740 + 342.25 Combine like terms: 1740 + 342.25 = 2082.25 342.25 + 37x + x2 = 2082.25 Factor a perfect square on the left side: (x + 18.5)(x + 18.5) = 2082.25 Calculate the square root of the right side: 45.631677594 Break this problem into two subproblems by setting (x + 18.5) equal to 45.631677594 and -45.631677594.Subproblem 1
x + 18.5 = 45.631677594 Simplifying x + 18.5 = 45.631677594 Reorder the terms: 18.5 + x = 45.631677594 Solving 18.5 + x = 45.631677594 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 = 45.631677594 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 45.631677594 + -18.5 x = 45.631677594 + -18.5 Combine like terms: 45.631677594 + -18.5 = 27.131677594 x = 27.131677594 Simplifying x = 27.131677594Subproblem 2
x + 18.5 = -45.631677594 Simplifying x + 18.5 = -45.631677594 Reorder the terms: 18.5 + x = -45.631677594 Solving 18.5 + x = -45.631677594 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 = -45.631677594 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -45.631677594 + -18.5 x = -45.631677594 + -18.5 Combine like terms: -45.631677594 + -18.5 = -64.131677594 x = -64.131677594 Simplifying x = -64.131677594Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.131677594, -64.131677594}
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