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Simplifying (x + -50) + (x * x) = 180 Reorder the terms: (-50 + x) + (x * x) = 180 Remove parenthesis around (-50 + x) -50 + x + (x * x) = 180 Multiply x * x -50 + x + (x2) = 180 -50 + x + x2 = 180 Solving -50 + x + x2 = 180 Solving for variable 'x'. Reorder the terms: -50 + -180 + x + x2 = 180 + -180 Combine like terms: -50 + -180 = -230 -230 + x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -230 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '230' to each side of the equation. -230 + x + 230 + x2 = 0 + 230 Reorder the terms: -230 + 230 + x + x2 = 0 + 230 Combine like terms: -230 + 230 = 0 0 + x + x2 = 0 + 230 x + x2 = 0 + 230 Combine like terms: 0 + 230 = 230 x + x2 = 230 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 230 + 0.25 Reorder the terms: 0.25 + x + x2 = 230 + 0.25 Combine like terms: 230 + 0.25 = 230.25 0.25 + x + x2 = 230.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 230.25 Calculate the square root of the right side: 15.173990905 Break this problem into two subproblems by setting (x + 0.5) equal to 15.173990905 and -15.173990905.Subproblem 1
x + 0.5 = 15.173990905 Simplifying x + 0.5 = 15.173990905 Reorder the terms: 0.5 + x = 15.173990905 Solving 0.5 + x = 15.173990905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 15.173990905 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 15.173990905 + -0.5 x = 15.173990905 + -0.5 Combine like terms: 15.173990905 + -0.5 = 14.673990905 x = 14.673990905 Simplifying x = 14.673990905Subproblem 2
x + 0.5 = -15.173990905 Simplifying x + 0.5 = -15.173990905 Reorder the terms: 0.5 + x = -15.173990905 Solving 0.5 + x = -15.173990905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -15.173990905 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -15.173990905 + -0.5 x = -15.173990905 + -0.5 Combine like terms: -15.173990905 + -0.5 = -15.673990905 x = -15.673990905 Simplifying x = -15.673990905Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.673990905, -15.673990905}
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