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Simplifying a2 + -40a + -1600 = 0 Reorder the terms: -1600 + -40a + a2 = 0 Solving -1600 + -40a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '1600' to each side of the equation. -1600 + -40a + 1600 + a2 = 0 + 1600 Reorder the terms: -1600 + 1600 + -40a + a2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + -40a + a2 = 0 + 1600 -40a + a2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 -40a + a2 = 1600 The a term is -40a. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40a + 400 + a2 = 1600 + 400 Reorder the terms: 400 + -40a + a2 = 1600 + 400 Combine like terms: 1600 + 400 = 2000 400 + -40a + a2 = 2000 Factor a perfect square on the left side: (a + -20)(a + -20) = 2000 Calculate the square root of the right side: 44.72135955 Break this problem into two subproblems by setting (a + -20) equal to 44.72135955 and -44.72135955.Subproblem 1
a + -20 = 44.72135955 Simplifying a + -20 = 44.72135955 Reorder the terms: -20 + a = 44.72135955 Solving -20 + a = 44.72135955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + a = 44.72135955 + 20 Combine like terms: -20 + 20 = 0 0 + a = 44.72135955 + 20 a = 44.72135955 + 20 Combine like terms: 44.72135955 + 20 = 64.72135955 a = 64.72135955 Simplifying a = 64.72135955Subproblem 2
a + -20 = -44.72135955 Simplifying a + -20 = -44.72135955 Reorder the terms: -20 + a = -44.72135955 Solving -20 + a = -44.72135955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + a = -44.72135955 + 20 Combine like terms: -20 + 20 = 0 0 + a = -44.72135955 + 20 a = -44.72135955 + 20 Combine like terms: -44.72135955 + 20 = -24.72135955 a = -24.72135955 Simplifying a = -24.72135955Solution
The solution to the problem is based on the solutions from the subproblems. a = {64.72135955, -24.72135955}
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