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Simplifying 2x2 + 17x + -448 = 0 Reorder the terms: -448 + 17x + 2x2 = 0 Solving -448 + 17x + 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'. -224 + 8.5x + x2 = 0 Move the constant term to the right: Add '224' to each side of the equation. -224 + 8.5x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + 8.5x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + 8.5x + x2 = 0 + 224 8.5x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 8.5x + x2 = 224 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 224 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 224 + 18.0625 Combine like terms: 224 + 18.0625 = 242.0625 18.0625 + 8.5x + x2 = 242.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 242.0625 Calculate the square root of the right side: 15.558357883 Break this problem into two subproblems by setting (x + 4.25) equal to 15.558357883 and -15.558357883.Subproblem 1
x + 4.25 = 15.558357883 Simplifying x + 4.25 = 15.558357883 Reorder the terms: 4.25 + x = 15.558357883 Solving 4.25 + x = 15.558357883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 15.558357883 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 15.558357883 + -4.25 x = 15.558357883 + -4.25 Combine like terms: 15.558357883 + -4.25 = 11.308357883 x = 11.308357883 Simplifying x = 11.308357883Subproblem 2
x + 4.25 = -15.558357883 Simplifying x + 4.25 = -15.558357883 Reorder the terms: 4.25 + x = -15.558357883 Solving 4.25 + x = -15.558357883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -15.558357883 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -15.558357883 + -4.25 x = -15.558357883 + -4.25 Combine like terms: -15.558357883 + -4.25 = -19.808357883 x = -19.808357883 Simplifying x = -19.808357883Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.308357883, -19.808357883}
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