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Simplifying 2a2 + 6a + -36 = 2 Reorder the terms: -36 + 6a + 2a2 = 2 Solving -36 + 6a + 2a2 = 2 Solving for variable 'a'. Reorder the terms: -36 + -2 + 6a + 2a2 = 2 + -2 Combine like terms: -36 + -2 = -38 -38 + 6a + 2a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -38 + 6a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + 3a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + 3a + a2)' equal to zero and attempt to solve: Simplifying -19 + 3a + a2 = 0 Solving -19 + 3a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 3a + 19 + a2 = 0 + 19 Reorder the terms: -19 + 19 + 3a + a2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 3a + a2 = 0 + 19 3a + a2 = 0 + 19 Combine like terms: 0 + 19 = 19 3a + a2 = 19 The a term is 3a. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3a + 2.25 + a2 = 19 + 2.25 Reorder the terms: 2.25 + 3a + a2 = 19 + 2.25 Combine like terms: 19 + 2.25 = 21.25 2.25 + 3a + a2 = 21.25 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (a + 1.5) equal to 4.609772229 and -4.609772229.Subproblem 1
a + 1.5 = 4.609772229 Simplifying a + 1.5 = 4.609772229 Reorder the terms: 1.5 + a = 4.609772229 Solving 1.5 + a = 4.609772229 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = 4.609772229 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 4.609772229 + -1.5 a = 4.609772229 + -1.5 Combine like terms: 4.609772229 + -1.5 = 3.109772229 a = 3.109772229 Simplifying a = 3.109772229Subproblem 2
a + 1.5 = -4.609772229 Simplifying a + 1.5 = -4.609772229 Reorder the terms: 1.5 + a = -4.609772229 Solving 1.5 + a = -4.609772229 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = -4.609772229 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -4.609772229 + -1.5 a = -4.609772229 + -1.5 Combine like terms: -4.609772229 + -1.5 = -6.109772229 a = -6.109772229 Simplifying a = -6.109772229Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.109772229, -6.109772229}Solution
a = {3.109772229, -6.109772229}
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