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Simplifying 2x2 + 17x + -108 = 0 Reorder the terms: -108 + 17x + 2x2 = 0 Solving -108 + 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'. -54 + 8.5x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + 8.5x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 8.5x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 8.5x + x2 = 0 + 54 8.5x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 8.5x + x2 = 54 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 = 54 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 54 + 18.0625 Combine like terms: 54 + 18.0625 = 72.0625 18.0625 + 8.5x + x2 = 72.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 72.0625 Calculate the square root of the right side: 8.488963423 Break this problem into two subproblems by setting (x + 4.25) equal to 8.488963423 and -8.488963423.Subproblem 1
x + 4.25 = 8.488963423 Simplifying x + 4.25 = 8.488963423 Reorder the terms: 4.25 + x = 8.488963423 Solving 4.25 + x = 8.488963423 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 = 8.488963423 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 8.488963423 + -4.25 x = 8.488963423 + -4.25 Combine like terms: 8.488963423 + -4.25 = 4.238963423 x = 4.238963423 Simplifying x = 4.238963423Subproblem 2
x + 4.25 = -8.488963423 Simplifying x + 4.25 = -8.488963423 Reorder the terms: 4.25 + x = -8.488963423 Solving 4.25 + x = -8.488963423 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 = -8.488963423 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -8.488963423 + -4.25 x = -8.488963423 + -4.25 Combine like terms: -8.488963423 + -4.25 = -12.738963423 x = -12.738963423 Simplifying x = -12.738963423Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.238963423, -12.738963423}
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