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Simplifying 20 + -1x = -10x2 + 200x + -250 Reorder the terms: 20 + -1x = -250 + 200x + -10x2 Solving 20 + -1x = -250 + 200x + -10x2 Solving for variable 'x'. Reorder the terms: 20 + 250 + -1x + -200x + 10x2 = -250 + 200x + -10x2 + 250 + -200x + 10x2 Combine like terms: 20 + 250 = 270 270 + -1x + -200x + 10x2 = -250 + 200x + -10x2 + 250 + -200x + 10x2 Combine like terms: -1x + -200x = -201x 270 + -201x + 10x2 = -250 + 200x + -10x2 + 250 + -200x + 10x2 Reorder the terms: 270 + -201x + 10x2 = -250 + 250 + 200x + -200x + -10x2 + 10x2 Combine like terms: -250 + 250 = 0 270 + -201x + 10x2 = 0 + 200x + -200x + -10x2 + 10x2 270 + -201x + 10x2 = 200x + -200x + -10x2 + 10x2 Combine like terms: 200x + -200x = 0 270 + -201x + 10x2 = 0 + -10x2 + 10x2 270 + -201x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 270 + -201x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 27 + -20.1x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -20.1x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -20.1x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -20.1x + x2 = 0 + -27 -20.1x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -20.1x + x2 = -27 The x term is -20.1x. Take half its coefficient (-10.05). Square it (101.0025) and add it to both sides. Add '101.0025' to each side of the equation. -20.1x + 101.0025 + x2 = -27 + 101.0025 Reorder the terms: 101.0025 + -20.1x + x2 = -27 + 101.0025 Combine like terms: -27 + 101.0025 = 74.0025 101.0025 + -20.1x + x2 = 74.0025 Factor a perfect square on the left side: (x + -10.05)(x + -10.05) = 74.0025 Calculate the square root of the right side: 8.602470575 Break this problem into two subproblems by setting (x + -10.05) equal to 8.602470575 and -8.602470575.Subproblem 1
x + -10.05 = 8.602470575 Simplifying x + -10.05 = 8.602470575 Reorder the terms: -10.05 + x = 8.602470575 Solving -10.05 + x = 8.602470575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.05' to each side of the equation. -10.05 + 10.05 + x = 8.602470575 + 10.05 Combine like terms: -10.05 + 10.05 = 0.00 0.00 + x = 8.602470575 + 10.05 x = 8.602470575 + 10.05 Combine like terms: 8.602470575 + 10.05 = 18.652470575 x = 18.652470575 Simplifying x = 18.652470575Subproblem 2
x + -10.05 = -8.602470575 Simplifying x + -10.05 = -8.602470575 Reorder the terms: -10.05 + x = -8.602470575 Solving -10.05 + x = -8.602470575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.05' to each side of the equation. -10.05 + 10.05 + x = -8.602470575 + 10.05 Combine like terms: -10.05 + 10.05 = 0.00 0.00 + x = -8.602470575 + 10.05 x = -8.602470575 + 10.05 Combine like terms: -8.602470575 + 10.05 = 1.447529425 x = 1.447529425 Simplifying x = 1.447529425Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.652470575, 1.447529425}
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