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Simplifying 180 + -1x = 5x(90 + -1x) 180 + -1x = (90 * 5x + -1x * 5x) 180 + -1x = (450x + -5x2) Solving 180 + -1x = 450x + -5x2 Solving for variable 'x'. Combine like terms: -1x + -450x = -451x 180 + -451x + 5x2 = 450x + -5x2 + -450x + 5x2 Reorder the terms: 180 + -451x + 5x2 = 450x + -450x + -5x2 + 5x2 Combine like terms: 450x + -450x = 0 180 + -451x + 5x2 = 0 + -5x2 + 5x2 180 + -451x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 180 + -451x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 36 + -90.2x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -90.2x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -90.2x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -90.2x + x2 = 0 + -36 -90.2x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -90.2x + x2 = -36 The x term is -90.2x. Take half its coefficient (-45.1). Square it (2034.01) and add it to both sides. Add '2034.01' to each side of the equation. -90.2x + 2034.01 + x2 = -36 + 2034.01 Reorder the terms: 2034.01 + -90.2x + x2 = -36 + 2034.01 Combine like terms: -36 + 2034.01 = 1998.01 2034.01 + -90.2x + x2 = 1998.01 Factor a perfect square on the left side: (x + -45.1)(x + -45.1) = 1998.01 Calculate the square root of the right side: 44.699105136 Break this problem into two subproblems by setting (x + -45.1) equal to 44.699105136 and -44.699105136.Subproblem 1
x + -45.1 = 44.699105136 Simplifying x + -45.1 = 44.699105136 Reorder the terms: -45.1 + x = 44.699105136 Solving -45.1 + x = 44.699105136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.1' to each side of the equation. -45.1 + 45.1 + x = 44.699105136 + 45.1 Combine like terms: -45.1 + 45.1 = 0.0 0.0 + x = 44.699105136 + 45.1 x = 44.699105136 + 45.1 Combine like terms: 44.699105136 + 45.1 = 89.799105136 x = 89.799105136 Simplifying x = 89.799105136Subproblem 2
x + -45.1 = -44.699105136 Simplifying x + -45.1 = -44.699105136 Reorder the terms: -45.1 + x = -44.699105136 Solving -45.1 + x = -44.699105136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.1' to each side of the equation. -45.1 + 45.1 + x = -44.699105136 + 45.1 Combine like terms: -45.1 + 45.1 = 0.0 0.0 + x = -44.699105136 + 45.1 x = -44.699105136 + 45.1 Combine like terms: -44.699105136 + 45.1 = 0.400894864 x = 0.400894864 Simplifying x = 0.400894864Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.799105136, 0.400894864}
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