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Simplifying (2a + -5)(2a + -5) = 60 Reorder the terms: (-5 + 2a)(2a + -5) = 60 Reorder the terms: (-5 + 2a)(-5 + 2a) = 60 Multiply (-5 + 2a) * (-5 + 2a) (-5(-5 + 2a) + 2a * (-5 + 2a)) = 60 ((-5 * -5 + 2a * -5) + 2a * (-5 + 2a)) = 60 ((25 + -10a) + 2a * (-5 + 2a)) = 60 (25 + -10a + (-5 * 2a + 2a * 2a)) = 60 (25 + -10a + (-10a + 4a2)) = 60 Combine like terms: -10a + -10a = -20a (25 + -20a + 4a2) = 60 Solving 25 + -20a + 4a2 = 60 Solving for variable 'a'. Reorder the terms: 25 + -60 + -20a + 4a2 = 60 + -60 Combine like terms: 25 + -60 = -35 -35 + -20a + 4a2 = 60 + -60 Combine like terms: 60 + -60 = 0 -35 + -20a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + -5a + a2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -5a + 8.75 + a2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -5a + a2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -5a + a2 = 0 + 8.75 -5a + a2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -5a + a2 = 8.75 The a term is -5a. 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. -5a + 6.25 + a2 = 8.75 + 6.25 Reorder the terms: 6.25 + -5a + a2 = 8.75 + 6.25 Combine like terms: 8.75 + 6.25 = 15 6.25 + -5a + a2 = 15 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (a + -2.5) equal to 3.872983346 and -3.872983346.Subproblem 1
a + -2.5 = 3.872983346 Simplifying a + -2.5 = 3.872983346 Reorder the terms: -2.5 + a = 3.872983346 Solving -2.5 + a = 3.872983346 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 3.872983346 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 3.872983346 + 2.5 a = 3.872983346 + 2.5 Combine like terms: 3.872983346 + 2.5 = 6.372983346 a = 6.372983346 Simplifying a = 6.372983346Subproblem 2
a + -2.5 = -3.872983346 Simplifying a + -2.5 = -3.872983346 Reorder the terms: -2.5 + a = -3.872983346 Solving -2.5 + a = -3.872983346 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -3.872983346 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -3.872983346 + 2.5 a = -3.872983346 + 2.5 Combine like terms: -3.872983346 + 2.5 = -1.372983346 a = -1.372983346 Simplifying a = -1.372983346Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.372983346, -1.372983346}
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