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Simplifying a(a + 5) = 44 Reorder the terms: a(5 + a) = 44 (5 * a + a * a) = 44 (5a + a2) = 44 Solving 5a + a2 = 44 Solving for variable 'a'. Reorder the terms: -44 + 5a + a2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + 5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 5a + 44 + a2 = 0 + 44 Reorder the terms: -44 + 44 + 5a + a2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 5a + a2 = 0 + 44 5a + a2 = 0 + 44 Combine like terms: 0 + 44 = 44 5a + a2 = 44 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 = 44 + 6.25 Reorder the terms: 6.25 + 5a + a2 = 44 + 6.25 Combine like terms: 44 + 6.25 = 50.25 6.25 + 5a + a2 = 50.25 Factor a perfect square on the left side: (a + 2.5)(a + 2.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (a + 2.5) equal to 7.088723439 and -7.088723439.Subproblem 1
a + 2.5 = 7.088723439 Simplifying a + 2.5 = 7.088723439 Reorder the terms: 2.5 + a = 7.088723439 Solving 2.5 + a = 7.088723439 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 = 7.088723439 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 7.088723439 + -2.5 a = 7.088723439 + -2.5 Combine like terms: 7.088723439 + -2.5 = 4.588723439 a = 4.588723439 Simplifying a = 4.588723439Subproblem 2
a + 2.5 = -7.088723439 Simplifying a + 2.5 = -7.088723439 Reorder the terms: 2.5 + a = -7.088723439 Solving 2.5 + a = -7.088723439 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 = -7.088723439 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -7.088723439 + -2.5 a = -7.088723439 + -2.5 Combine like terms: -7.088723439 + -2.5 = -9.588723439 a = -9.588723439 Simplifying a = -9.588723439Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.588723439, -9.588723439}
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