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Simplifying x(x + -50) = 180 Reorder the terms: x(-50 + x) = 180 (-50 * x + x * x) = 180 (-50x + x2) = 180 Solving -50x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -50x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -50x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -50x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -50x + x2 = 0 + 180 -50x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -50x + x2 = 180 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 180 + 625 Reorder the terms: 625 + -50x + x2 = 180 + 625 Combine like terms: 180 + 625 = 805 625 + -50x + x2 = 805 Factor a perfect square on the left side: (x + -25)(x + -25) = 805 Calculate the square root of the right side: 28.372521918 Break this problem into two subproblems by setting (x + -25) equal to 28.372521918 and -28.372521918.Subproblem 1
x + -25 = 28.372521918 Simplifying x + -25 = 28.372521918 Reorder the terms: -25 + x = 28.372521918 Solving -25 + x = 28.372521918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 28.372521918 + 25 Combine like terms: -25 + 25 = 0 0 + x = 28.372521918 + 25 x = 28.372521918 + 25 Combine like terms: 28.372521918 + 25 = 53.372521918 x = 53.372521918 Simplifying x = 53.372521918Subproblem 2
x + -25 = -28.372521918 Simplifying x + -25 = -28.372521918 Reorder the terms: -25 + x = -28.372521918 Solving -25 + x = -28.372521918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -28.372521918 + 25 Combine like terms: -25 + 25 = 0 0 + x = -28.372521918 + 25 x = -28.372521918 + 25 Combine like terms: -28.372521918 + 25 = -3.372521918 x = -3.372521918 Simplifying x = -3.372521918Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.372521918, -3.372521918}
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