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Simplifying (x + -6) + (2x + 34)(x) = 180 Reorder the terms: (-6 + x) + (2x + 34)(x) = 180 Remove parenthesis around (-6 + x) -6 + x + (2x + 34)(x) = 180 Reorder the terms: -6 + x + (34 + 2x)(x) = 180 Reorder the terms for easier multiplication: -6 + x + x(34 + 2x) = 180 -6 + x + (34 * x + 2x * x) = 180 -6 + x + (34x + 2x2) = 180 Combine like terms: x + 34x = 35x -6 + 35x + 2x2 = 180 Solving -6 + 35x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -6 + -180 + 35x + 2x2 = 180 + -180 Combine like terms: -6 + -180 = -186 -186 + 35x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -186 + 35x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -93 + 17.5x + x2 = 0 Move the constant term to the right: Add '93' to each side of the equation. -93 + 17.5x + 93 + x2 = 0 + 93 Reorder the terms: -93 + 93 + 17.5x + x2 = 0 + 93 Combine like terms: -93 + 93 = 0 0 + 17.5x + x2 = 0 + 93 17.5x + x2 = 0 + 93 Combine like terms: 0 + 93 = 93 17.5x + x2 = 93 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 = 93 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 93 + 76.5625 Combine like terms: 93 + 76.5625 = 169.5625 76.5625 + 17.5x + x2 = 169.5625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 169.5625 Calculate the square root of the right side: 13.021616643 Break this problem into two subproblems by setting (x + 8.75) equal to 13.021616643 and -13.021616643.Subproblem 1
x + 8.75 = 13.021616643 Simplifying x + 8.75 = 13.021616643 Reorder the terms: 8.75 + x = 13.021616643 Solving 8.75 + x = 13.021616643 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 = 13.021616643 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 13.021616643 + -8.75 x = 13.021616643 + -8.75 Combine like terms: 13.021616643 + -8.75 = 4.271616643 x = 4.271616643 Simplifying x = 4.271616643Subproblem 2
x + 8.75 = -13.021616643 Simplifying x + 8.75 = -13.021616643 Reorder the terms: 8.75 + x = -13.021616643 Solving 8.75 + x = -13.021616643 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 = -13.021616643 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -13.021616643 + -8.75 x = -13.021616643 + -8.75 Combine like terms: -13.021616643 + -8.75 = -21.771616643 x = -21.771616643 Simplifying x = -21.771616643Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.271616643, -21.771616643}
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