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Simplifying 2x2 + -7x + -250 = 0 Reorder the terms: -250 + -7x + 2x2 = 0 Solving -250 + -7x + 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 + -3.5x + x2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + -3.5x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + -3.5x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -3.5x + x2 = 0 + 125 -3.5x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 -3.5x + x2 = 125 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 125 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 125 + 3.0625 Combine like terms: 125 + 3.0625 = 128.0625 3.0625 + -3.5x + x2 = 128.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 128.0625 Calculate the square root of the right side: 11.316470298 Break this problem into two subproblems by setting (x + -1.75) equal to 11.316470298 and -11.316470298.Subproblem 1
x + -1.75 = 11.316470298 Simplifying x + -1.75 = 11.316470298 Reorder the terms: -1.75 + x = 11.316470298 Solving -1.75 + x = 11.316470298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 11.316470298 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 11.316470298 + 1.75 x = 11.316470298 + 1.75 Combine like terms: 11.316470298 + 1.75 = 13.066470298 x = 13.066470298 Simplifying x = 13.066470298Subproblem 2
x + -1.75 = -11.316470298 Simplifying x + -1.75 = -11.316470298 Reorder the terms: -1.75 + x = -11.316470298 Solving -1.75 + x = -11.316470298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -11.316470298 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -11.316470298 + 1.75 x = -11.316470298 + 1.75 Combine like terms: -11.316470298 + 1.75 = -9.566470298 x = -9.566470298 Simplifying x = -9.566470298Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.066470298, -9.566470298}
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