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Simplifying x2 + -46x + 485 = 0 Reorder the terms: 485 + -46x + x2 = 0 Solving 485 + -46x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-485' to each side of the equation. 485 + -46x + -485 + x2 = 0 + -485 Reorder the terms: 485 + -485 + -46x + x2 = 0 + -485 Combine like terms: 485 + -485 = 0 0 + -46x + x2 = 0 + -485 -46x + x2 = 0 + -485 Combine like terms: 0 + -485 = -485 -46x + x2 = -485 The x term is -46x. Take half its coefficient (-23). Square it (529) and add it to both sides. Add '529' to each side of the equation. -46x + 529 + x2 = -485 + 529 Reorder the terms: 529 + -46x + x2 = -485 + 529 Combine like terms: -485 + 529 = 44 529 + -46x + x2 = 44 Factor a perfect square on the left side: (x + -23)(x + -23) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + -23) equal to 6.633249581 and -6.633249581.Subproblem 1
x + -23 = 6.633249581 Simplifying x + -23 = 6.633249581 Reorder the terms: -23 + x = 6.633249581 Solving -23 + x = 6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = 6.633249581 + 23 Combine like terms: -23 + 23 = 0 0 + x = 6.633249581 + 23 x = 6.633249581 + 23 Combine like terms: 6.633249581 + 23 = 29.633249581 x = 29.633249581 Simplifying x = 29.633249581Subproblem 2
x + -23 = -6.633249581 Simplifying x + -23 = -6.633249581 Reorder the terms: -23 + x = -6.633249581 Solving -23 + x = -6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = -6.633249581 + 23 Combine like terms: -23 + 23 = 0 0 + x = -6.633249581 + 23 x = -6.633249581 + 23 Combine like terms: -6.633249581 + 23 = 16.366750419 x = 16.366750419 Simplifying x = 16.366750419Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.633249581, 16.366750419}
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