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Simplifying x = 12x2 + -184x + 529 Reorder the terms: x = 529 + -184x + 12x2 Solving x = 529 + -184x + 12x2 Solving for variable 'x'. Reorder the terms: -529 + x + 184x + -12x2 = 529 + -184x + 12x2 + -529 + 184x + -12x2 Combine like terms: x + 184x = 185x -529 + 185x + -12x2 = 529 + -184x + 12x2 + -529 + 184x + -12x2 Reorder the terms: -529 + 185x + -12x2 = 529 + -529 + -184x + 184x + 12x2 + -12x2 Combine like terms: 529 + -529 = 0 -529 + 185x + -12x2 = 0 + -184x + 184x + 12x2 + -12x2 -529 + 185x + -12x2 = -184x + 184x + 12x2 + -12x2 Combine like terms: -184x + 184x = 0 -529 + 185x + -12x2 = 0 + 12x2 + -12x2 -529 + 185x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -529 + 185x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 44.08333333 + -15.41666667x + x2 = 0 Move the constant term to the right: Add '-44.08333333' to each side of the equation. 44.08333333 + -15.41666667x + -44.08333333 + x2 = 0 + -44.08333333 Reorder the terms: 44.08333333 + -44.08333333 + -15.41666667x + x2 = 0 + -44.08333333 Combine like terms: 44.08333333 + -44.08333333 = 0.00000000 0.00000000 + -15.41666667x + x2 = 0 + -44.08333333 -15.41666667x + x2 = 0 + -44.08333333 Combine like terms: 0 + -44.08333333 = -44.08333333 -15.41666667x + x2 = -44.08333333 The x term is -15.41666667x. Take half its coefficient (-7.708333335). Square it (59.41840280) and add it to both sides. Add '59.41840280' to each side of the equation. -15.41666667x + 59.41840280 + x2 = -44.08333333 + 59.41840280 Reorder the terms: 59.41840280 + -15.41666667x + x2 = -44.08333333 + 59.41840280 Combine like terms: -44.08333333 + 59.41840280 = 15.33506947 59.41840280 + -15.41666667x + x2 = 15.33506947 Factor a perfect square on the left side: (x + -7.708333335)(x + -7.708333335) = 15.33506947 Calculate the square root of the right side: 3.91600172 Break this problem into two subproblems by setting (x + -7.708333335) equal to 3.91600172 and -3.91600172.Subproblem 1
x + -7.708333335 = 3.91600172 Simplifying x + -7.708333335 = 3.91600172 Reorder the terms: -7.708333335 + x = 3.91600172 Solving -7.708333335 + x = 3.91600172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.708333335' to each side of the equation. -7.708333335 + 7.708333335 + x = 3.91600172 + 7.708333335 Combine like terms: -7.708333335 + 7.708333335 = 0.000000000 0.000000000 + x = 3.91600172 + 7.708333335 x = 3.91600172 + 7.708333335 Combine like terms: 3.91600172 + 7.708333335 = 11.624335055 x = 11.624335055 Simplifying x = 11.624335055Subproblem 2
x + -7.708333335 = -3.91600172 Simplifying x + -7.708333335 = -3.91600172 Reorder the terms: -7.708333335 + x = -3.91600172 Solving -7.708333335 + x = -3.91600172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.708333335' to each side of the equation. -7.708333335 + 7.708333335 + x = -3.91600172 + 7.708333335 Combine like terms: -7.708333335 + 7.708333335 = 0.000000000 0.000000000 + x = -3.91600172 + 7.708333335 x = -3.91600172 + 7.708333335 Combine like terms: -3.91600172 + 7.708333335 = 3.792331615 x = 3.792331615 Simplifying x = 3.792331615Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.624335055, 3.792331615}
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