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Simplifying 2a2 + 22a = 36 Reorder the terms: 22a + 2a2 = 36 Solving 22a + 2a2 = 36 Solving for variable 'a'. Reorder the terms: -36 + 22a + 2a2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 22a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 11a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + 11a + a2)' equal to zero and attempt to solve: Simplifying -18 + 11a + a2 = 0 Solving -18 + 11a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 11a + 18 + a2 = 0 + 18 Reorder the terms: -18 + 18 + 11a + a2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 11a + a2 = 0 + 18 11a + a2 = 0 + 18 Combine like terms: 0 + 18 = 18 11a + a2 = 18 The a term is 11a. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11a + 30.25 + a2 = 18 + 30.25 Reorder the terms: 30.25 + 11a + a2 = 18 + 30.25 Combine like terms: 18 + 30.25 = 48.25 30.25 + 11a + a2 = 48.25 Factor a perfect square on the left side: (a + 5.5)(a + 5.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (a + 5.5) equal to 6.946221995 and -6.946221995.Subproblem 1
a + 5.5 = 6.946221995 Simplifying a + 5.5 = 6.946221995 Reorder the terms: 5.5 + a = 6.946221995 Solving 5.5 + a = 6.946221995 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + a = 6.946221995 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = 6.946221995 + -5.5 a = 6.946221995 + -5.5 Combine like terms: 6.946221995 + -5.5 = 1.446221995 a = 1.446221995 Simplifying a = 1.446221995Subproblem 2
a + 5.5 = -6.946221995 Simplifying a + 5.5 = -6.946221995 Reorder the terms: 5.5 + a = -6.946221995 Solving 5.5 + a = -6.946221995 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + a = -6.946221995 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = -6.946221995 + -5.5 a = -6.946221995 + -5.5 Combine like terms: -6.946221995 + -5.5 = -12.446221995 a = -12.446221995 Simplifying a = -12.446221995Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.446221995, -12.446221995}Solution
a = {1.446221995, -12.446221995}
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