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Simplifying a2 + -60a + 180 = 0 Reorder the terms: 180 + -60a + a2 = 0 Solving 180 + -60a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-180' to each side of the equation. 180 + -60a + -180 + a2 = 0 + -180 Reorder the terms: 180 + -180 + -60a + a2 = 0 + -180 Combine like terms: 180 + -180 = 0 0 + -60a + a2 = 0 + -180 -60a + a2 = 0 + -180 Combine like terms: 0 + -180 = -180 -60a + a2 = -180 The a term is -60a. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60a + 900 + a2 = -180 + 900 Reorder the terms: 900 + -60a + a2 = -180 + 900 Combine like terms: -180 + 900 = 720 900 + -60a + a2 = 720 Factor a perfect square on the left side: (a + -30)(a + -30) = 720 Calculate the square root of the right side: 26.83281573 Break this problem into two subproblems by setting (a + -30) equal to 26.83281573 and -26.83281573.Subproblem 1
a + -30 = 26.83281573 Simplifying a + -30 = 26.83281573 Reorder the terms: -30 + a = 26.83281573 Solving -30 + a = 26.83281573 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + a = 26.83281573 + 30 Combine like terms: -30 + 30 = 0 0 + a = 26.83281573 + 30 a = 26.83281573 + 30 Combine like terms: 26.83281573 + 30 = 56.83281573 a = 56.83281573 Simplifying a = 56.83281573Subproblem 2
a + -30 = -26.83281573 Simplifying a + -30 = -26.83281573 Reorder the terms: -30 + a = -26.83281573 Solving -30 + a = -26.83281573 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + a = -26.83281573 + 30 Combine like terms: -30 + 30 = 0 0 + a = -26.83281573 + 30 a = -26.83281573 + 30 Combine like terms: -26.83281573 + 30 = 3.16718427 a = 3.16718427 Simplifying a = 3.16718427Solution
The solution to the problem is based on the solutions from the subproblems. a = {56.83281573, 3.16718427}
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