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Simplifying 2a(a + 10) = 44 Reorder the terms: 2a(10 + a) = 44 (10 * 2a + a * 2a) = 44 (20a + 2a2) = 44 Solving 20a + 2a2 = 44 Solving for variable 'a'. Reorder the terms: -44 + 20a + 2a2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + 20a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-22 + 10a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-22 + 10a + a2)' equal to zero and attempt to solve: Simplifying -22 + 10a + a2 = 0 Solving -22 + 10a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 10a + 22 + a2 = 0 + 22 Reorder the terms: -22 + 22 + 10a + a2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 10a + a2 = 0 + 22 10a + a2 = 0 + 22 Combine like terms: 0 + 22 = 22 10a + a2 = 22 The a term is 10a. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10a + 25 + a2 = 22 + 25 Reorder the terms: 25 + 10a + a2 = 22 + 25 Combine like terms: 22 + 25 = 47 25 + 10a + a2 = 47 Factor a perfect square on the left side: (a + 5)(a + 5) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (a + 5) equal to 6.8556546 and -6.8556546.Subproblem 1
a + 5 = 6.8556546 Simplifying a + 5 = 6.8556546 Reorder the terms: 5 + a = 6.8556546 Solving 5 + a = 6.8556546 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 6.8556546 + -5 Combine like terms: 5 + -5 = 0 0 + a = 6.8556546 + -5 a = 6.8556546 + -5 Combine like terms: 6.8556546 + -5 = 1.8556546 a = 1.8556546 Simplifying a = 1.8556546Subproblem 2
a + 5 = -6.8556546 Simplifying a + 5 = -6.8556546 Reorder the terms: 5 + a = -6.8556546 Solving 5 + a = -6.8556546 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = -6.8556546 + -5 Combine like terms: 5 + -5 = 0 0 + a = -6.8556546 + -5 a = -6.8556546 + -5 Combine like terms: -6.8556546 + -5 = -11.8556546 a = -11.8556546 Simplifying a = -11.8556546Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.8556546, -11.8556546}Solution
a = {1.8556546, -11.8556546}
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