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Simplifying a + 18a2 + -106 = -10 Reorder the terms: -106 + a + 18a2 = -10 Solving -106 + a + 18a2 = -10 Solving for variable 'a'. Reorder the terms: -106 + 10 + a + 18a2 = -10 + 10 Combine like terms: -106 + 10 = -96 -96 + a + 18a2 = -10 + 10 Combine like terms: -10 + 10 = 0 -96 + a + 18a2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -5.333333333 + 0.05555555556a + a2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + 0.05555555556a + 5.333333333 + a2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + 0.05555555556a + a2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + 0.05555555556a + a2 = 0 + 5.333333333 0.05555555556a + a2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 0.05555555556a + a2 = 5.333333333 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.05555555556a + 0.25 + a2 = 5.333333333 + 0.25 Reorder the terms: 0.25 + 0.05555555556a + a2 = 5.333333333 + 0.25 Combine like terms: 5.333333333 + 0.25 = 5.583333333 0.25 + 0.05555555556a + a2 = 5.583333333 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 5.583333333 Calculate the square root of the right side: 2.362907813 Break this problem into two subproblems by setting (a + 0.5) equal to 2.362907813 and -2.362907813.Subproblem 1
a + 0.5 = 2.362907813 Simplifying a + 0.5 = 2.362907813 Reorder the terms: 0.5 + a = 2.362907813 Solving 0.5 + a = 2.362907813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 2.362907813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 2.362907813 + -0.5 a = 2.362907813 + -0.5 Combine like terms: 2.362907813 + -0.5 = 1.862907813 a = 1.862907813 Simplifying a = 1.862907813Subproblem 2
a + 0.5 = -2.362907813 Simplifying a + 0.5 = -2.362907813 Reorder the terms: 0.5 + a = -2.362907813 Solving 0.5 + a = -2.362907813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -2.362907813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -2.362907813 + -0.5 a = -2.362907813 + -0.5 Combine like terms: -2.362907813 + -0.5 = -2.862907813 a = -2.862907813 Simplifying a = -2.862907813Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.862907813, -2.862907813}
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