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Simplifying 5a2 + -5a + 1 = 0 Reorder the terms: 1 + -5a + 5a2 = 0 Solving 1 + -5a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -1a + a2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1a + -0.2 + a2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1a + a2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1a + a2 = 0 + -0.2 -1a + a2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1a + a2 = -0.2 The a term is -1a. 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. -1a + 0.25 + a2 = -0.2 + 0.25 Reorder the terms: 0.25 + -1a + a2 = -0.2 + 0.25 Combine like terms: -0.2 + 0.25 = 0.05 0.25 + -1a + a2 = 0.05 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 0.05 Calculate the square root of the right side: 0.223606798 Break this problem into two subproblems by setting (a + -0.5) equal to 0.223606798 and -0.223606798.Subproblem 1
a + -0.5 = 0.223606798 Simplifying a + -0.5 = 0.223606798 Reorder the terms: -0.5 + a = 0.223606798 Solving -0.5 + a = 0.223606798 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 = 0.223606798 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 0.223606798 + 0.5 a = 0.223606798 + 0.5 Combine like terms: 0.223606798 + 0.5 = 0.723606798 a = 0.723606798 Simplifying a = 0.723606798Subproblem 2
a + -0.5 = -0.223606798 Simplifying a + -0.5 = -0.223606798 Reorder the terms: -0.5 + a = -0.223606798 Solving -0.5 + a = -0.223606798 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 = -0.223606798 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -0.223606798 + 0.5 a = -0.223606798 + 0.5 Combine like terms: -0.223606798 + 0.5 = 0.276393202 a = 0.276393202 Simplifying a = 0.276393202Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.723606798, 0.276393202}
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