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Simplifying 8a2 + -1 = 6a Reorder the terms: -1 + 8a2 = 6a Solving -1 + 8a2 = 6a Solving for variable 'a'. Reorder the terms: -1 + -6a + 8a2 = 6a + -6a Combine like terms: 6a + -6a = 0 -1 + -6a + 8a2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -0.75a + a2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.75a + 0.125 + a2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.75a + a2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.75a + a2 = 0 + 0.125 -0.75a + a2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.75a + a2 = 0.125 The a term is -0.75a. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75a + 0.140625 + a2 = 0.125 + 0.140625 Reorder the terms: 0.140625 + -0.75a + a2 = 0.125 + 0.140625 Combine like terms: 0.125 + 0.140625 = 0.265625 0.140625 + -0.75a + a2 = 0.265625 Factor a perfect square on the left side: (a + -0.375)(a + -0.375) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (a + -0.375) equal to 0.515388203 and -0.515388203.Subproblem 1
a + -0.375 = 0.515388203 Simplifying a + -0.375 = 0.515388203 Reorder the terms: -0.375 + a = 0.515388203 Solving -0.375 + a = 0.515388203 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + a = 0.515388203 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + a = 0.515388203 + 0.375 a = 0.515388203 + 0.375 Combine like terms: 0.515388203 + 0.375 = 0.890388203 a = 0.890388203 Simplifying a = 0.890388203Subproblem 2
a + -0.375 = -0.515388203 Simplifying a + -0.375 = -0.515388203 Reorder the terms: -0.375 + a = -0.515388203 Solving -0.375 + a = -0.515388203 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + a = -0.515388203 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + a = -0.515388203 + 0.375 a = -0.515388203 + 0.375 Combine like terms: -0.515388203 + 0.375 = -0.140388203 a = -0.140388203 Simplifying a = -0.140388203Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.890388203, -0.140388203}
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