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Simplifying x2 + -46x = -180 Reorder the terms: -46x + x2 = -180 Solving -46x + x2 = -180 Solving for variable 'x'. Reorder the terms: 180 + -46x + x2 = -180 + 180 Combine like terms: -180 + 180 = 0 180 + -46x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-180' to each side of the equation. 180 + -46x + -180 + x2 = 0 + -180 Reorder the terms: 180 + -180 + -46x + x2 = 0 + -180 Combine like terms: 180 + -180 = 0 0 + -46x + x2 = 0 + -180 -46x + x2 = 0 + -180 Combine like terms: 0 + -180 = -180 -46x + x2 = -180 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 = -180 + 529 Reorder the terms: 529 + -46x + x2 = -180 + 529 Combine like terms: -180 + 529 = 349 529 + -46x + x2 = 349 Factor a perfect square on the left side: (x + -23)(x + -23) = 349 Calculate the square root of the right side: 18.681541692 Break this problem into two subproblems by setting (x + -23) equal to 18.681541692 and -18.681541692.Subproblem 1
x + -23 = 18.681541692 Simplifying x + -23 = 18.681541692 Reorder the terms: -23 + x = 18.681541692 Solving -23 + x = 18.681541692 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 = 18.681541692 + 23 Combine like terms: -23 + 23 = 0 0 + x = 18.681541692 + 23 x = 18.681541692 + 23 Combine like terms: 18.681541692 + 23 = 41.681541692 x = 41.681541692 Simplifying x = 41.681541692Subproblem 2
x + -23 = -18.681541692 Simplifying x + -23 = -18.681541692 Reorder the terms: -23 + x = -18.681541692 Solving -23 + x = -18.681541692 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 = -18.681541692 + 23 Combine like terms: -23 + 23 = 0 0 + x = -18.681541692 + 23 x = -18.681541692 + 23 Combine like terms: -18.681541692 + 23 = 4.318458308 x = 4.318458308 Simplifying x = 4.318458308Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.681541692, 4.318458308}
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