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Simplifying 2x2 + -9x + -500 = 0 Reorder the terms: -500 + -9x + 2x2 = 0 Solving -500 + -9x + 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'. -250 + -4.5x + x2 = 0 Move the constant term to the right: Add '250' to each side of the equation. -250 + -4.5x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + -4.5x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + -4.5x + x2 = 0 + 250 -4.5x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 -4.5x + x2 = 250 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 250 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 250 + 5.0625 Combine like terms: 250 + 5.0625 = 255.0625 5.0625 + -4.5x + x2 = 255.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 255.0625 Calculate the square root of the right side: 15.970676254 Break this problem into two subproblems by setting (x + -2.25) equal to 15.970676254 and -15.970676254.Subproblem 1
x + -2.25 = 15.970676254 Simplifying x + -2.25 = 15.970676254 Reorder the terms: -2.25 + x = 15.970676254 Solving -2.25 + x = 15.970676254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 15.970676254 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 15.970676254 + 2.25 x = 15.970676254 + 2.25 Combine like terms: 15.970676254 + 2.25 = 18.220676254 x = 18.220676254 Simplifying x = 18.220676254Subproblem 2
x + -2.25 = -15.970676254 Simplifying x + -2.25 = -15.970676254 Reorder the terms: -2.25 + x = -15.970676254 Solving -2.25 + x = -15.970676254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -15.970676254 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -15.970676254 + 2.25 x = -15.970676254 + 2.25 Combine like terms: -15.970676254 + 2.25 = -13.720676254 x = -13.720676254 Simplifying x = -13.720676254Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.220676254, -13.720676254}
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