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Simplifying 74 = 37x + -1x2 Solving 74 = 37x + -1x2 Solving for variable 'x'. Reorder the terms: 74 + -37x + x2 = 37x + -37x + -1x2 + x2 Combine like terms: 37x + -37x = 0 74 + -37x + x2 = 0 + -1x2 + x2 74 + -37x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 74 + -37x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-74' to each side of the equation. 74 + -37x + -74 + x2 = 0 + -74 Reorder the terms: 74 + -74 + -37x + x2 = 0 + -74 Combine like terms: 74 + -74 = 0 0 + -37x + x2 = 0 + -74 -37x + x2 = 0 + -74 Combine like terms: 0 + -74 = -74 -37x + x2 = -74 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 = -74 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -74 + 342.25 Combine like terms: -74 + 342.25 = 268.25 342.25 + -37x + x2 = 268.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 268.25 Calculate the square root of the right side: 16.378339354 Break this problem into two subproblems by setting (x + -18.5) equal to 16.378339354 and -16.378339354.Subproblem 1
x + -18.5 = 16.378339354 Simplifying x + -18.5 = 16.378339354 Reorder the terms: -18.5 + x = 16.378339354 Solving -18.5 + x = 16.378339354 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 = 16.378339354 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 16.378339354 + 18.5 x = 16.378339354 + 18.5 Combine like terms: 16.378339354 + 18.5 = 34.878339354 x = 34.878339354 Simplifying x = 34.878339354Subproblem 2
x + -18.5 = -16.378339354 Simplifying x + -18.5 = -16.378339354 Reorder the terms: -18.5 + x = -16.378339354 Solving -18.5 + x = -16.378339354 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 = -16.378339354 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -16.378339354 + 18.5 x = -16.378339354 + 18.5 Combine like terms: -16.378339354 + 18.5 = 2.121660646 x = 2.121660646 Simplifying x = 2.121660646Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.878339354, 2.121660646}
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