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Simplifying x2 + 11x + 30.25 = 498.25 Reorder the terms: 30.25 + 11x + x2 = 498.25 Solving 30.25 + 11x + x2 = 498.25 Solving for variable 'x'. Reorder the terms: 30.25 + -498.25 + 11x + x2 = 498.25 + -498.25 Combine like terms: 30.25 + -498.25 = -468 -468 + 11x + x2 = 498.25 + -498.25 Combine like terms: 498.25 + -498.25 = 0.00 -468 + 11x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '468' to each side of the equation. -468 + 11x + 468 + x2 = 0.00 + 468 Reorder the terms: -468 + 468 + 11x + x2 = 0.00 + 468 Combine like terms: -468 + 468 = 0 0 + 11x + x2 = 0.00 + 468 11x + x2 = 0.00 + 468 Combine like terms: 0.00 + 468 = 468 11x + x2 = 468 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 468 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 468 + 30.25 Combine like terms: 468 + 30.25 = 498.25 30.25 + 11x + x2 = 498.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 498.25 Calculate the square root of the right side: 22.321514286 Break this problem into two subproblems by setting (x + 5.5) equal to 22.321514286 and -22.321514286.Subproblem 1
x + 5.5 = 22.321514286 Simplifying x + 5.5 = 22.321514286 Reorder the terms: 5.5 + x = 22.321514286 Solving 5.5 + x = 22.321514286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 22.321514286 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 22.321514286 + -5.5 x = 22.321514286 + -5.5 Combine like terms: 22.321514286 + -5.5 = 16.821514286 x = 16.821514286 Simplifying x = 16.821514286Subproblem 2
x + 5.5 = -22.321514286 Simplifying x + 5.5 = -22.321514286 Reorder the terms: 5.5 + x = -22.321514286 Solving 5.5 + x = -22.321514286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -22.321514286 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -22.321514286 + -5.5 x = -22.321514286 + -5.5 Combine like terms: -22.321514286 + -5.5 = -27.821514286 x = -27.821514286 Simplifying x = -27.821514286Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.821514286, -27.821514286}
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