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Simplifying 0.2x2 + -174x + 3550 = 0 Reorder the terms: 3550 + -174x + 0.2x2 = 0 Solving 3550 + -174x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 17750 + -870x + x2 = 0 Move the constant term to the right: Add '-17750' to each side of the equation. 17750 + -870x + -17750 + x2 = 0 + -17750 Reorder the terms: 17750 + -17750 + -870x + x2 = 0 + -17750 Combine like terms: 17750 + -17750 = 0 0 + -870x + x2 = 0 + -17750 -870x + x2 = 0 + -17750 Combine like terms: 0 + -17750 = -17750 -870x + x2 = -17750 The x term is -870x. Take half its coefficient (-435). Square it (189225) and add it to both sides. Add '189225' to each side of the equation. -870x + 189225 + x2 = -17750 + 189225 Reorder the terms: 189225 + -870x + x2 = -17750 + 189225 Combine like terms: -17750 + 189225 = 171475 189225 + -870x + x2 = 171475 Factor a perfect square on the left side: (x + -435)(x + -435) = 171475 Calculate the square root of the right side: 414.095399636 Break this problem into two subproblems by setting (x + -435) equal to 414.095399636 and -414.095399636.Subproblem 1
x + -435 = 414.095399636 Simplifying x + -435 = 414.095399636 Reorder the terms: -435 + x = 414.095399636 Solving -435 + x = 414.095399636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '435' to each side of the equation. -435 + 435 + x = 414.095399636 + 435 Combine like terms: -435 + 435 = 0 0 + x = 414.095399636 + 435 x = 414.095399636 + 435 Combine like terms: 414.095399636 + 435 = 849.095399636 x = 849.095399636 Simplifying x = 849.095399636Subproblem 2
x + -435 = -414.095399636 Simplifying x + -435 = -414.095399636 Reorder the terms: -435 + x = -414.095399636 Solving -435 + x = -414.095399636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '435' to each side of the equation. -435 + 435 + x = -414.095399636 + 435 Combine like terms: -435 + 435 = 0 0 + x = -414.095399636 + 435 x = -414.095399636 + 435 Combine like terms: -414.095399636 + 435 = 20.904600364 x = 20.904600364 Simplifying x = 20.904600364Solution
The solution to the problem is based on the solutions from the subproblems. x = {849.095399636, 20.904600364}
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