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Simplifying 2x2 + -33x + -250 = 0 Reorder the terms: -250 + -33x + 2x2 = 0 Solving -250 + -33x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -125 + -16.5x + x2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + -16.5x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + -16.5x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -16.5x + x2 = 0 + 125 -16.5x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 -16.5x + x2 = 125 The x term is -16.5x. Take half its coefficient (-8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. -16.5x + 68.0625 + x2 = 125 + 68.0625 Reorder the terms: 68.0625 + -16.5x + x2 = 125 + 68.0625 Combine like terms: 125 + 68.0625 = 193.0625 68.0625 + -16.5x + x2 = 193.0625 Factor a perfect square on the left side: (x + -8.25)(x + -8.25) = 193.0625 Calculate the square root of the right side: 13.894693232 Break this problem into two subproblems by setting (x + -8.25) equal to 13.894693232 and -13.894693232.Subproblem 1
x + -8.25 = 13.894693232 Simplifying x + -8.25 = 13.894693232 Reorder the terms: -8.25 + x = 13.894693232 Solving -8.25 + x = 13.894693232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = 13.894693232 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = 13.894693232 + 8.25 x = 13.894693232 + 8.25 Combine like terms: 13.894693232 + 8.25 = 22.144693232 x = 22.144693232 Simplifying x = 22.144693232Subproblem 2
x + -8.25 = -13.894693232 Simplifying x + -8.25 = -13.894693232 Reorder the terms: -8.25 + x = -13.894693232 Solving -8.25 + x = -13.894693232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = -13.894693232 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = -13.894693232 + 8.25 x = -13.894693232 + 8.25 Combine like terms: -13.894693232 + 8.25 = -5.644693232 x = -5.644693232 Simplifying x = -5.644693232Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.144693232, -5.644693232}
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