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Simplifying 180 = x(x + -5) Reorder the terms: 180 = x(-5 + x) 180 = (-5 * x + x * x) 180 = (-5x + x2) Solving 180 = -5x + x2 Solving for variable 'x'. Reorder the terms: 180 + 5x + -1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 180 + 5x + -1x2 = 0 + x2 + -1x2 180 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 180 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -180 + -5x + x2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + -5x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -5x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -5x + x2 = 0 + 180 -5x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -5x + x2 = 180 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 180 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 180 + 6.25 Combine like terms: 180 + 6.25 = 186.25 6.25 + -5x + x2 = 186.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 186.25 Calculate the square root of the right side: 13.647344064 Break this problem into two subproblems by setting (x + -2.5) equal to 13.647344064 and -13.647344064.Subproblem 1
x + -2.5 = 13.647344064 Simplifying x + -2.5 = 13.647344064 Reorder the terms: -2.5 + x = 13.647344064 Solving -2.5 + x = 13.647344064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 13.647344064 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 13.647344064 + 2.5 x = 13.647344064 + 2.5 Combine like terms: 13.647344064 + 2.5 = 16.147344064 x = 16.147344064 Simplifying x = 16.147344064Subproblem 2
x + -2.5 = -13.647344064 Simplifying x + -2.5 = -13.647344064 Reorder the terms: -2.5 + x = -13.647344064 Solving -2.5 + x = -13.647344064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -13.647344064 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -13.647344064 + 2.5 x = -13.647344064 + 2.5 Combine like terms: -13.647344064 + 2.5 = -11.147344064 x = -11.147344064 Simplifying x = -11.147344064Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.147344064, -11.147344064}
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