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Simplifying 2x(180 + -1x) = 27 (180 * 2x + -1x * 2x) = 27 (360x + -2x2) = 27 Solving 360x + -2x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + 360x + -2x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 360x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 13.5 + -180x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -180x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -180x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -180x + x2 = 0 + -13.5 -180x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -180x + x2 = -13.5 The x term is -180x. Take half its coefficient (-90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. -180x + 8100 + x2 = -13.5 + 8100 Reorder the terms: 8100 + -180x + x2 = -13.5 + 8100 Combine like terms: -13.5 + 8100 = 8086.5 8100 + -180x + x2 = 8086.5 Factor a perfect square on the left side: (x + -90)(x + -90) = 8086.5 Calculate the square root of the right side: 89.924968724 Break this problem into two subproblems by setting (x + -90) equal to 89.924968724 and -89.924968724.Subproblem 1
x + -90 = 89.924968724 Simplifying x + -90 = 89.924968724 Reorder the terms: -90 + x = 89.924968724 Solving -90 + x = 89.924968724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 89.924968724 + 90 Combine like terms: -90 + 90 = 0 0 + x = 89.924968724 + 90 x = 89.924968724 + 90 Combine like terms: 89.924968724 + 90 = 179.924968724 x = 179.924968724 Simplifying x = 179.924968724Subproblem 2
x + -90 = -89.924968724 Simplifying x + -90 = -89.924968724 Reorder the terms: -90 + x = -89.924968724 Solving -90 + x = -89.924968724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = -89.924968724 + 90 Combine like terms: -90 + 90 = 0 0 + x = -89.924968724 + 90 x = -89.924968724 + 90 Combine like terms: -89.924968724 + 90 = 0.075031276 x = 0.075031276 Simplifying x = 0.075031276Solution
The solution to the problem is based on the solutions from the subproblems. x = {179.924968724, 0.075031276}
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