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Simplifying 37x + x2 = 226.6 Solving 37x + x2 = 226.6 Solving for variable 'x'. Reorder the terms: -226.6 + 37x + x2 = 226.6 + -226.6 Combine like terms: 226.6 + -226.6 = 0.0 -226.6 + 37x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '226.6' to each side of the equation. -226.6 + 37x + 226.6 + x2 = 0.0 + 226.6 Reorder the terms: -226.6 + 226.6 + 37x + x2 = 0.0 + 226.6 Combine like terms: -226.6 + 226.6 = 0.0 0.0 + 37x + x2 = 0.0 + 226.6 37x + x2 = 0.0 + 226.6 Combine like terms: 0.0 + 226.6 = 226.6 37x + x2 = 226.6 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 = 226.6 + 342.25 Reorder the terms: 342.25 + 37x + x2 = 226.6 + 342.25 Combine like terms: 226.6 + 342.25 = 568.85 342.25 + 37x + x2 = 568.85 Factor a perfect square on the left side: (x + 18.5)(x + 18.5) = 568.85 Calculate the square root of the right side: 23.850576513 Break this problem into two subproblems by setting (x + 18.5) equal to 23.850576513 and -23.850576513.Subproblem 1
x + 18.5 = 23.850576513 Simplifying x + 18.5 = 23.850576513 Reorder the terms: 18.5 + x = 23.850576513 Solving 18.5 + x = 23.850576513 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 = 23.850576513 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 23.850576513 + -18.5 x = 23.850576513 + -18.5 Combine like terms: 23.850576513 + -18.5 = 5.350576513 x = 5.350576513 Simplifying x = 5.350576513Subproblem 2
x + 18.5 = -23.850576513 Simplifying x + 18.5 = -23.850576513 Reorder the terms: 18.5 + x = -23.850576513 Solving 18.5 + x = -23.850576513 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 = -23.850576513 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -23.850576513 + -18.5 x = -23.850576513 + -18.5 Combine like terms: -23.850576513 + -18.5 = -42.350576513 x = -42.350576513 Simplifying x = -42.350576513Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.350576513, -42.350576513}
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