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Simplifying 8a2 = 4a + 3 Reorder the terms: 8a2 = 3 + 4a Solving 8a2 = 3 + 4a Solving for variable 'a'. Reorder the terms: -3 + -4a + 8a2 = 3 + 4a + -3 + -4a Reorder the terms: -3 + -4a + 8a2 = 3 + -3 + 4a + -4a Combine like terms: 3 + -3 = 0 -3 + -4a + 8a2 = 0 + 4a + -4a -3 + -4a + 8a2 = 4a + -4a Combine like terms: 4a + -4a = 0 -3 + -4a + 8a2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -0.5a + a2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.5a + 0.375 + a2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.5a + a2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.5a + a2 = 0 + 0.375 -0.5a + a2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.5a + a2 = 0.375 The a term is -0.5a. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5a + 0.0625 + a2 = 0.375 + 0.0625 Reorder the terms: 0.0625 + -0.5a + a2 = 0.375 + 0.0625 Combine like terms: 0.375 + 0.0625 = 0.4375 0.0625 + -0.5a + a2 = 0.4375 Factor a perfect square on the left side: (a + -0.25)(a + -0.25) = 0.4375 Calculate the square root of the right side: 0.661437828 Break this problem into two subproblems by setting (a + -0.25) equal to 0.661437828 and -0.661437828.Subproblem 1
a + -0.25 = 0.661437828 Simplifying a + -0.25 = 0.661437828 Reorder the terms: -0.25 + a = 0.661437828 Solving -0.25 + a = 0.661437828 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = 0.661437828 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 0.661437828 + 0.25 a = 0.661437828 + 0.25 Combine like terms: 0.661437828 + 0.25 = 0.911437828 a = 0.911437828 Simplifying a = 0.911437828Subproblem 2
a + -0.25 = -0.661437828 Simplifying a + -0.25 = -0.661437828 Reorder the terms: -0.25 + a = -0.661437828 Solving -0.25 + a = -0.661437828 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = -0.661437828 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -0.661437828 + 0.25 a = -0.661437828 + 0.25 Combine like terms: -0.661437828 + 0.25 = -0.411437828 a = -0.411437828 Simplifying a = -0.411437828Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.911437828, -0.411437828}
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