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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 = 709 529 + -46x + x2 = 709 Factor a perfect square on the left side: (x + -23)(x + -23) = 709 Calculate the square root of the right side: 26.627053911 Break this problem into two subproblems by setting (x + -23) equal to 26.627053911 and -26.627053911.Subproblem 1
x + -23 = 26.627053911 Simplifying x + -23 = 26.627053911 Reorder the terms: -23 + x = 26.627053911 Solving -23 + x = 26.627053911 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 = 26.627053911 + 23 Combine like terms: -23 + 23 = 0 0 + x = 26.627053911 + 23 x = 26.627053911 + 23 Combine like terms: 26.627053911 + 23 = 49.627053911 x = 49.627053911 Simplifying x = 49.627053911Subproblem 2
x + -23 = -26.627053911 Simplifying x + -23 = -26.627053911 Reorder the terms: -23 + x = -26.627053911 Solving -23 + x = -26.627053911 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 = -26.627053911 + 23 Combine like terms: -23 + 23 = 0 0 + x = -26.627053911 + 23 x = -26.627053911 + 23 Combine like terms: -26.627053911 + 23 = -3.627053911 x = -3.627053911 Simplifying x = -3.627053911Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.627053911, -3.627053911}
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