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Simplifying x2 + -60x + 180 = 0 Reorder the terms: 180 + -60x + x2 = 0 Solving 180 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-180' to each side of the equation. 180 + -60x + -180 + x2 = 0 + -180 Reorder the terms: 180 + -180 + -60x + x2 = 0 + -180 Combine like terms: 180 + -180 = 0 0 + -60x + x2 = 0 + -180 -60x + x2 = 0 + -180 Combine like terms: 0 + -180 = -180 -60x + x2 = -180 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 = -180 + 900 Reorder the terms: 900 + -60x + x2 = -180 + 900 Combine like terms: -180 + 900 = 720 900 + -60x + x2 = 720 Factor a perfect square on the left side: (x + -30)(x + -30) = 720 Calculate the square root of the right side: 26.83281573 Break this problem into two subproblems by setting (x + -30) equal to 26.83281573 and -26.83281573.Subproblem 1
x + -30 = 26.83281573 Simplifying x + -30 = 26.83281573 Reorder the terms: -30 + x = 26.83281573 Solving -30 + x = 26.83281573 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 = 26.83281573 + 30 Combine like terms: -30 + 30 = 0 0 + x = 26.83281573 + 30 x = 26.83281573 + 30 Combine like terms: 26.83281573 + 30 = 56.83281573 x = 56.83281573 Simplifying x = 56.83281573Subproblem 2
x + -30 = -26.83281573 Simplifying x + -30 = -26.83281573 Reorder the terms: -30 + x = -26.83281573 Solving -30 + x = -26.83281573 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 = -26.83281573 + 30 Combine like terms: -30 + 30 = 0 0 + x = -26.83281573 + 30 x = -26.83281573 + 30 Combine like terms: -26.83281573 + 30 = 3.16718427 x = 3.16718427 Simplifying x = 3.16718427Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.83281573, 3.16718427}
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