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Simplifying x + x(x + -27) = 180 Reorder the terms: x + x(-27 + x) = 180 x + (-27 * x + x * x) = 180 x + (-27x + x2) = 180 Combine like terms: x + -27x = -26x -26x + x2 = 180 Solving -26x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -26x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -26x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -26x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -26x + x2 = 0 + 180 -26x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -26x + x2 = 180 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = 180 + 169 Reorder the terms: 169 + -26x + x2 = 180 + 169 Combine like terms: 180 + 169 = 349 169 + -26x + x2 = 349 Factor a perfect square on the left side: (x + -13)(x + -13) = 349 Calculate the square root of the right side: 18.681541692 Break this problem into two subproblems by setting (x + -13) equal to 18.681541692 and -18.681541692.Subproblem 1
x + -13 = 18.681541692 Simplifying x + -13 = 18.681541692 Reorder the terms: -13 + x = 18.681541692 Solving -13 + x = 18.681541692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 18.681541692 + 13 Combine like terms: -13 + 13 = 0 0 + x = 18.681541692 + 13 x = 18.681541692 + 13 Combine like terms: 18.681541692 + 13 = 31.681541692 x = 31.681541692 Simplifying x = 31.681541692Subproblem 2
x + -13 = -18.681541692 Simplifying x + -13 = -18.681541692 Reorder the terms: -13 + x = -18.681541692 Solving -13 + x = -18.681541692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -18.681541692 + 13 Combine like terms: -13 + 13 = 0 0 + x = -18.681541692 + 13 x = -18.681541692 + 13 Combine like terms: -18.681541692 + 13 = -5.681541692 x = -5.681541692 Simplifying x = -5.681541692Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.681541692, -5.681541692}
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