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Simplifying 35x + -764 = 23 + -2x2 Reorder the terms: -764 + 35x = 23 + -2x2 Solving -764 + 35x = 23 + -2x2 Solving for variable 'x'. Reorder the terms: -764 + -23 + 35x + 2x2 = 23 + -2x2 + -23 + 2x2 Combine like terms: -764 + -23 = -787 -787 + 35x + 2x2 = 23 + -2x2 + -23 + 2x2 Reorder the terms: -787 + 35x + 2x2 = 23 + -23 + -2x2 + 2x2 Combine like terms: 23 + -23 = 0 -787 + 35x + 2x2 = 0 + -2x2 + 2x2 -787 + 35x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -787 + 35x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -393.5 + 17.5x + x2 = 0 Move the constant term to the right: Add '393.5' to each side of the equation. -393.5 + 17.5x + 393.5 + x2 = 0 + 393.5 Reorder the terms: -393.5 + 393.5 + 17.5x + x2 = 0 + 393.5 Combine like terms: -393.5 + 393.5 = 0.0 0.0 + 17.5x + x2 = 0 + 393.5 17.5x + x2 = 0 + 393.5 Combine like terms: 0 + 393.5 = 393.5 17.5x + x2 = 393.5 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 = 393.5 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 393.5 + 76.5625 Combine like terms: 393.5 + 76.5625 = 470.0625 76.5625 + 17.5x + x2 = 470.0625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 470.0625 Calculate the square root of the right side: 21.680924796 Break this problem into two subproblems by setting (x + 8.75) equal to 21.680924796 and -21.680924796.Subproblem 1
x + 8.75 = 21.680924796 Simplifying x + 8.75 = 21.680924796 Reorder the terms: 8.75 + x = 21.680924796 Solving 8.75 + x = 21.680924796 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 = 21.680924796 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 21.680924796 + -8.75 x = 21.680924796 + -8.75 Combine like terms: 21.680924796 + -8.75 = 12.930924796 x = 12.930924796 Simplifying x = 12.930924796Subproblem 2
x + 8.75 = -21.680924796 Simplifying x + 8.75 = -21.680924796 Reorder the terms: 8.75 + x = -21.680924796 Solving 8.75 + x = -21.680924796 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 = -21.680924796 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -21.680924796 + -8.75 x = -21.680924796 + -8.75 Combine like terms: -21.680924796 + -8.75 = -30.430924796 x = -30.430924796 Simplifying x = -30.430924796Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.930924796, -30.430924796}
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