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Simplifying x2 + -46x + 17 = 0 Reorder the terms: 17 + -46x + x2 = 0 Solving 17 + -46x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -46x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + -46x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -46x + x2 = 0 + -17 -46x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 -46x + x2 = -17 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 = -17 + 529 Reorder the terms: 529 + -46x + x2 = -17 + 529 Combine like terms: -17 + 529 = 512 529 + -46x + x2 = 512 Factor a perfect square on the left side: (x + -23)(x + -23) = 512 Calculate the square root of the right side: 22.627416998 Break this problem into two subproblems by setting (x + -23) equal to 22.627416998 and -22.627416998.Subproblem 1
x + -23 = 22.627416998 Simplifying x + -23 = 22.627416998 Reorder the terms: -23 + x = 22.627416998 Solving -23 + x = 22.627416998 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 = 22.627416998 + 23 Combine like terms: -23 + 23 = 0 0 + x = 22.627416998 + 23 x = 22.627416998 + 23 Combine like terms: 22.627416998 + 23 = 45.627416998 x = 45.627416998 Simplifying x = 45.627416998Subproblem 2
x + -23 = -22.627416998 Simplifying x + -23 = -22.627416998 Reorder the terms: -23 + x = -22.627416998 Solving -23 + x = -22.627416998 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 = -22.627416998 + 23 Combine like terms: -23 + 23 = 0 0 + x = -22.627416998 + 23 x = -22.627416998 + 23 Combine like terms: -22.627416998 + 23 = 0.372583002 x = 0.372583002 Simplifying x = 0.372583002Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.627416998, 0.372583002}
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