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Simplifying x(x) + 180x + -8952064 = 0 Multiply x * x x2 + 180x + -8952064 = 0 Reorder the terms: -8952064 + 180x + x2 = 0 Solving -8952064 + 180x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8952064' to each side of the equation. -8952064 + 180x + 8952064 + x2 = 0 + 8952064 Reorder the terms: -8952064 + 8952064 + 180x + x2 = 0 + 8952064 Combine like terms: -8952064 + 8952064 = 0 0 + 180x + x2 = 0 + 8952064 180x + x2 = 0 + 8952064 Combine like terms: 0 + 8952064 = 8952064 180x + x2 = 8952064 The x term is 180x. Take half its coefficient (90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. 180x + 8100 + x2 = 8952064 + 8100 Reorder the terms: 8100 + 180x + x2 = 8952064 + 8100 Combine like terms: 8952064 + 8100 = 8960164 8100 + 180x + x2 = 8960164 Factor a perfect square on the left side: (x + 90)(x + 90) = 8960164 Calculate the square root of the right side: 2993.353303571 Break this problem into two subproblems by setting (x + 90) equal to 2993.353303571 and -2993.353303571.Subproblem 1
x + 90 = 2993.353303571 Simplifying x + 90 = 2993.353303571 Reorder the terms: 90 + x = 2993.353303571 Solving 90 + x = 2993.353303571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + x = 2993.353303571 + -90 Combine like terms: 90 + -90 = 0 0 + x = 2993.353303571 + -90 x = 2993.353303571 + -90 Combine like terms: 2993.353303571 + -90 = 2903.353303571 x = 2903.353303571 Simplifying x = 2903.353303571Subproblem 2
x + 90 = -2993.353303571 Simplifying x + 90 = -2993.353303571 Reorder the terms: 90 + x = -2993.353303571 Solving 90 + x = -2993.353303571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + x = -2993.353303571 + -90 Combine like terms: 90 + -90 = 0 0 + x = -2993.353303571 + -90 x = -2993.353303571 + -90 Combine like terms: -2993.353303571 + -90 = -3083.353303571 x = -3083.353303571 Simplifying x = -3083.353303571Solution
The solution to the problem is based on the solutions from the subproblems. x = {2903.353303571, -3083.353303571}
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