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Simplifying 2(x2) + -70x + 485 = 0 Reorder the terms: 485 + -70x + 2x2 = 0 Solving 485 + -70x + 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'. 242.5 + -35x + x2 = 0 Move the constant term to the right: Add '-242.5' to each side of the equation. 242.5 + -35x + -242.5 + x2 = 0 + -242.5 Reorder the terms: 242.5 + -242.5 + -35x + x2 = 0 + -242.5 Combine like terms: 242.5 + -242.5 = 0.0 0.0 + -35x + x2 = 0 + -242.5 -35x + x2 = 0 + -242.5 Combine like terms: 0 + -242.5 = -242.5 -35x + x2 = -242.5 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = -242.5 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -242.5 + 306.25 Combine like terms: -242.5 + 306.25 = 63.75 306.25 + -35x + x2 = 63.75 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 63.75 Calculate the square root of the right side: 7.984359711 Break this problem into two subproblems by setting (x + -17.5) equal to 7.984359711 and -7.984359711.Subproblem 1
x + -17.5 = 7.984359711 Simplifying x + -17.5 = 7.984359711 Reorder the terms: -17.5 + x = 7.984359711 Solving -17.5 + x = 7.984359711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 7.984359711 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 7.984359711 + 17.5 x = 7.984359711 + 17.5 Combine like terms: 7.984359711 + 17.5 = 25.484359711 x = 25.484359711 Simplifying x = 25.484359711Subproblem 2
x + -17.5 = -7.984359711 Simplifying x + -17.5 = -7.984359711 Reorder the terms: -17.5 + x = -7.984359711 Solving -17.5 + x = -7.984359711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -7.984359711 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -7.984359711 + 17.5 x = -7.984359711 + 17.5 Combine like terms: -7.984359711 + 17.5 = 9.515640289 x = 9.515640289 Simplifying x = 9.515640289Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.484359711, 9.515640289}
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