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Simplifying 8a2 + -65a + 5 = 0 Reorder the terms: 5 + -65a + 8a2 = 0 Solving 5 + -65a + 8a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + -8.125a + a2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -8.125a + -0.625 + a2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -8.125a + a2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -8.125a + a2 = 0 + -0.625 -8.125a + a2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -8.125a + a2 = -0.625 The a term is -8.125a. Take half its coefficient (-4.0625). Square it (16.50390625) and add it to both sides. Add '16.50390625' to each side of the equation. -8.125a + 16.50390625 + a2 = -0.625 + 16.50390625 Reorder the terms: 16.50390625 + -8.125a + a2 = -0.625 + 16.50390625 Combine like terms: -0.625 + 16.50390625 = 15.87890625 16.50390625 + -8.125a + a2 = 15.87890625 Factor a perfect square on the left side: (a + -4.0625)(a + -4.0625) = 15.87890625 Calculate the square root of the right side: 3.984834532 Break this problem into two subproblems by setting (a + -4.0625) equal to 3.984834532 and -3.984834532.Subproblem 1
a + -4.0625 = 3.984834532 Simplifying a + -4.0625 = 3.984834532 Reorder the terms: -4.0625 + a = 3.984834532 Solving -4.0625 + a = 3.984834532 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.0625' to each side of the equation. -4.0625 + 4.0625 + a = 3.984834532 + 4.0625 Combine like terms: -4.0625 + 4.0625 = 0.0000 0.0000 + a = 3.984834532 + 4.0625 a = 3.984834532 + 4.0625 Combine like terms: 3.984834532 + 4.0625 = 8.047334532 a = 8.047334532 Simplifying a = 8.047334532Subproblem 2
a + -4.0625 = -3.984834532 Simplifying a + -4.0625 = -3.984834532 Reorder the terms: -4.0625 + a = -3.984834532 Solving -4.0625 + a = -3.984834532 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.0625' to each side of the equation. -4.0625 + 4.0625 + a = -3.984834532 + 4.0625 Combine like terms: -4.0625 + 4.0625 = 0.0000 0.0000 + a = -3.984834532 + 4.0625 a = -3.984834532 + 4.0625 Combine like terms: -3.984834532 + 4.0625 = 0.077665468 a = 0.077665468 Simplifying a = 0.077665468Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.047334532, 0.077665468}
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