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Simplifying 2x2 + 35x + -117 = 0 Reorder the terms: -117 + 35x + 2x2 = 0 Solving -117 + 35x + 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'. -58.5 + 17.5x + x2 = 0 Move the constant term to the right: Add '58.5' to each side of the equation. -58.5 + 17.5x + 58.5 + x2 = 0 + 58.5 Reorder the terms: -58.5 + 58.5 + 17.5x + x2 = 0 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + 17.5x + x2 = 0 + 58.5 17.5x + x2 = 0 + 58.5 Combine like terms: 0 + 58.5 = 58.5 17.5x + x2 = 58.5 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 = 58.5 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 58.5 + 76.5625 Combine like terms: 58.5 + 76.5625 = 135.0625 76.5625 + 17.5x + x2 = 135.0625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 135.0625 Calculate the square root of the right side: 11.621639299 Break this problem into two subproblems by setting (x + 8.75) equal to 11.621639299 and -11.621639299.Subproblem 1
x + 8.75 = 11.621639299 Simplifying x + 8.75 = 11.621639299 Reorder the terms: 8.75 + x = 11.621639299 Solving 8.75 + x = 11.621639299 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 = 11.621639299 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 11.621639299 + -8.75 x = 11.621639299 + -8.75 Combine like terms: 11.621639299 + -8.75 = 2.871639299 x = 2.871639299 Simplifying x = 2.871639299Subproblem 2
x + 8.75 = -11.621639299 Simplifying x + 8.75 = -11.621639299 Reorder the terms: 8.75 + x = -11.621639299 Solving 8.75 + x = -11.621639299 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 = -11.621639299 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -11.621639299 + -8.75 x = -11.621639299 + -8.75 Combine like terms: -11.621639299 + -8.75 = -20.371639299 x = -20.371639299 Simplifying x = -20.371639299Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.871639299, -20.371639299}
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