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Simplifying 2a2 + -15a + -18 = 0 Reorder the terms: -18 + -15a + 2a2 = 0 Solving -18 + -15a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9 + -7.5a + a2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -7.5a + 9 + a2 = 0 + 9 Reorder the terms: -9 + 9 + -7.5a + a2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -7.5a + a2 = 0 + 9 -7.5a + a2 = 0 + 9 Combine like terms: 0 + 9 = 9 -7.5a + a2 = 9 The a term is -7.5a. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5a + 14.0625 + a2 = 9 + 14.0625 Reorder the terms: 14.0625 + -7.5a + a2 = 9 + 14.0625 Combine like terms: 9 + 14.0625 = 23.0625 14.0625 + -7.5a + a2 = 23.0625 Factor a perfect square on the left side: (a + -3.75)(a + -3.75) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (a + -3.75) equal to 4.802343178 and -4.802343178.Subproblem 1
a + -3.75 = 4.802343178 Simplifying a + -3.75 = 4.802343178 Reorder the terms: -3.75 + a = 4.802343178 Solving -3.75 + a = 4.802343178 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + a = 4.802343178 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + a = 4.802343178 + 3.75 a = 4.802343178 + 3.75 Combine like terms: 4.802343178 + 3.75 = 8.552343178 a = 8.552343178 Simplifying a = 8.552343178Subproblem 2
a + -3.75 = -4.802343178 Simplifying a + -3.75 = -4.802343178 Reorder the terms: -3.75 + a = -4.802343178 Solving -3.75 + a = -4.802343178 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + a = -4.802343178 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + a = -4.802343178 + 3.75 a = -4.802343178 + 3.75 Combine like terms: -4.802343178 + 3.75 = -1.052343178 a = -1.052343178 Simplifying a = -1.052343178Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.552343178, -1.052343178}
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