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Simplifying 2a2 + -20a + 27 = 0 Reorder the terms: 27 + -20a + 2a2 = 0 Solving 27 + -20a + 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'. 13.5 + -10a + a2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -10a + -13.5 + a2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -10a + a2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -10a + a2 = 0 + -13.5 -10a + a2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -10a + a2 = -13.5 The a term is -10a. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10a + 25 + a2 = -13.5 + 25 Reorder the terms: 25 + -10a + a2 = -13.5 + 25 Combine like terms: -13.5 + 25 = 11.5 25 + -10a + a2 = 11.5 Factor a perfect square on the left side: (a + -5)(a + -5) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (a + -5) equal to 3.391164992 and -3.391164992.Subproblem 1
a + -5 = 3.391164992 Simplifying a + -5 = 3.391164992 Reorder the terms: -5 + a = 3.391164992 Solving -5 + a = 3.391164992 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 3.391164992 + 5 Combine like terms: -5 + 5 = 0 0 + a = 3.391164992 + 5 a = 3.391164992 + 5 Combine like terms: 3.391164992 + 5 = 8.391164992 a = 8.391164992 Simplifying a = 8.391164992Subproblem 2
a + -5 = -3.391164992 Simplifying a + -5 = -3.391164992 Reorder the terms: -5 + a = -3.391164992 Solving -5 + a = -3.391164992 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = -3.391164992 + 5 Combine like terms: -5 + 5 = 0 0 + a = -3.391164992 + 5 a = -3.391164992 + 5 Combine like terms: -3.391164992 + 5 = 1.608835008 a = 1.608835008 Simplifying a = 1.608835008Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.391164992, 1.608835008}
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