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Simplifying 2a2 + 16a = 36 Reorder the terms: 16a + 2a2 = 36 Solving 16a + 2a2 = 36 Solving for variable 'a'. Reorder the terms: -36 + 16a + 2a2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 16a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 8a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + 8a + a2)' equal to zero and attempt to solve: Simplifying -18 + 8a + a2 = 0 Solving -18 + 8a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 8a + 18 + a2 = 0 + 18 Reorder the terms: -18 + 18 + 8a + a2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 8a + a2 = 0 + 18 8a + a2 = 0 + 18 Combine like terms: 0 + 18 = 18 8a + a2 = 18 The a term is 8a. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8a + 16 + a2 = 18 + 16 Reorder the terms: 16 + 8a + a2 = 18 + 16 Combine like terms: 18 + 16 = 34 16 + 8a + a2 = 34 Factor a perfect square on the left side: (a + 4)(a + 4) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (a + 4) equal to 5.830951895 and -5.830951895.Subproblem 1
a + 4 = 5.830951895 Simplifying a + 4 = 5.830951895 Reorder the terms: 4 + a = 5.830951895 Solving 4 + a = 5.830951895 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = 5.830951895 + -4 Combine like terms: 4 + -4 = 0 0 + a = 5.830951895 + -4 a = 5.830951895 + -4 Combine like terms: 5.830951895 + -4 = 1.830951895 a = 1.830951895 Simplifying a = 1.830951895Subproblem 2
a + 4 = -5.830951895 Simplifying a + 4 = -5.830951895 Reorder the terms: 4 + a = -5.830951895 Solving 4 + a = -5.830951895 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = -5.830951895 + -4 Combine like terms: 4 + -4 = 0 0 + a = -5.830951895 + -4 a = -5.830951895 + -4 Combine like terms: -5.830951895 + -4 = -9.830951895 a = -9.830951895 Simplifying a = -9.830951895Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.830951895, -9.830951895}Solution
a = {1.830951895, -9.830951895}
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