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Simplifying x2 + 60x + -1800 = 0 Reorder the terms: -1800 + 60x + x2 = 0 Solving -1800 + 60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1800' to each side of the equation. -1800 + 60x + 1800 + x2 = 0 + 1800 Reorder the terms: -1800 + 1800 + 60x + x2 = 0 + 1800 Combine like terms: -1800 + 1800 = 0 0 + 60x + x2 = 0 + 1800 60x + x2 = 0 + 1800 Combine like terms: 0 + 1800 = 1800 60x + x2 = 1800 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = 1800 + 900 Reorder the terms: 900 + 60x + x2 = 1800 + 900 Combine like terms: 1800 + 900 = 2700 900 + 60x + x2 = 2700 Factor a perfect square on the left side: (x + 30)(x + 30) = 2700 Calculate the square root of the right side: 51.961524227 Break this problem into two subproblems by setting (x + 30) equal to 51.961524227 and -51.961524227.Subproblem 1
x + 30 = 51.961524227 Simplifying x + 30 = 51.961524227 Reorder the terms: 30 + x = 51.961524227 Solving 30 + x = 51.961524227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 51.961524227 + -30 Combine like terms: 30 + -30 = 0 0 + x = 51.961524227 + -30 x = 51.961524227 + -30 Combine like terms: 51.961524227 + -30 = 21.961524227 x = 21.961524227 Simplifying x = 21.961524227Subproblem 2
x + 30 = -51.961524227 Simplifying x + 30 = -51.961524227 Reorder the terms: 30 + x = -51.961524227 Solving 30 + x = -51.961524227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -51.961524227 + -30 Combine like terms: 30 + -30 = 0 0 + x = -51.961524227 + -30 x = -51.961524227 + -30 Combine like terms: -51.961524227 + -30 = -81.961524227 x = -81.961524227 Simplifying x = -81.961524227Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.961524227, -81.961524227}
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