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Simplifying 0 = x2 + 17.5x + -50 Reorder the terms: 0 = -50 + 17.5x + x2 Solving 0 = -50 + 17.5x + x2 Solving for variable 'x'. Combine like terms: 0 + 50 = 50 50 + -17.5x + -1x2 = -50 + 17.5x + x2 + 50 + -17.5x + -1x2 Reorder the terms: 50 + -17.5x + -1x2 = -50 + 50 + 17.5x + -17.5x + x2 + -1x2 Combine like terms: -50 + 50 = 0 50 + -17.5x + -1x2 = 0 + 17.5x + -17.5x + x2 + -1x2 50 + -17.5x + -1x2 = 17.5x + -17.5x + x2 + -1x2 Combine like terms: 17.5x + -17.5x = 0.0 50 + -17.5x + -1x2 = 0.0 + x2 + -1x2 50 + -17.5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 50 + -17.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + 17.5x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 17.5x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 17.5x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 17.5x + x2 = 0 + 50 17.5x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 17.5x + x2 = 50 The x term is 17.5x. Take half its coefficient (8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. 17.5x + 76.5625 + x2 = 50 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 50 + 76.5625 Combine like terms: 50 + 76.5625 = 126.5625 76.5625 + 17.5x + x2 = 126.5625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 126.5625 Calculate the square root of the right side: 11.25 Break this problem into two subproblems by setting (x + 8.75) equal to 11.25 and -11.25.Subproblem 1
x + 8.75 = 11.25 Simplifying x + 8.75 = 11.25 Reorder the terms: 8.75 + x = 11.25 Solving 8.75 + x = 11.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = 11.25 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 11.25 + -8.75 x = 11.25 + -8.75 Combine like terms: 11.25 + -8.75 = 2.5 x = 2.5 Simplifying x = 2.5Subproblem 2
x + 8.75 = -11.25 Simplifying x + 8.75 = -11.25 Reorder the terms: 8.75 + x = -11.25 Solving 8.75 + x = -11.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = -11.25 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -11.25 + -8.75 x = -11.25 + -8.75 Combine like terms: -11.25 + -8.75 = -20 x = -20 Simplifying x = -20Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5, -20}
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