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Simplifying -0.5x2 = -17x + -17.5 Reorder the terms: -0.5x2 = -17.5 + -17x Solving -0.5x2 = -17.5 + -17x Solving for variable 'x'. Reorder the terms: 17.5 + 17x + -0.5x2 = -17.5 + -17x + 17.5 + 17x Reorder the terms: 17.5 + 17x + -0.5x2 = -17.5 + 17.5 + -17x + 17x Combine like terms: -17.5 + 17.5 = 0.0 17.5 + 17x + -0.5x2 = 0.0 + -17x + 17x 17.5 + 17x + -0.5x2 = -17x + 17x Combine like terms: -17x + 17x = 0 17.5 + 17x + -0.5x2 = 0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -35 + -34x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -34x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -34x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -34x + x2 = 0 + 35 -34x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -34x + x2 = 35 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = 35 + 289 Reorder the terms: 289 + -34x + x2 = 35 + 289 Combine like terms: 35 + 289 = 324 289 + -34x + x2 = 324 Factor a perfect square on the left side: (x + -17)(x + -17) = 324 Calculate the square root of the right side: 18 Break this problem into two subproblems by setting (x + -17) equal to 18 and -18.Subproblem 1
x + -17 = 18 Simplifying x + -17 = 18 Reorder the terms: -17 + x = 18 Solving -17 + x = 18 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 18 + 17 Combine like terms: -17 + 17 = 0 0 + x = 18 + 17 x = 18 + 17 Combine like terms: 18 + 17 = 35 x = 35 Simplifying x = 35Subproblem 2
x + -17 = -18 Simplifying x + -17 = -18 Reorder the terms: -17 + x = -18 Solving -17 + x = -18 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -18 + 17 Combine like terms: -17 + 17 = 0 0 + x = -18 + 17 x = -18 + 17 Combine like terms: -18 + 17 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {35, -1}
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