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Simplifying 8a2 + a + -1.68 = 0 Reorder the terms: -1.68 + a + 8a2 = 0 Solving -1.68 + a + 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'. -0.21 + 0.125a + a2 = 0 Move the constant term to the right: Add '0.21' to each side of the equation. -0.21 + 0.125a + 0.21 + a2 = 0 + 0.21 Reorder the terms: -0.21 + 0.21 + 0.125a + a2 = 0 + 0.21 Combine like terms: -0.21 + 0.21 = 0.00 0.00 + 0.125a + a2 = 0 + 0.21 0.125a + a2 = 0 + 0.21 Combine like terms: 0 + 0.21 = 0.21 0.125a + a2 = 0.21 The a term is a. 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. 0.125a + 0.25 + a2 = 0.21 + 0.25 Reorder the terms: 0.25 + 0.125a + a2 = 0.21 + 0.25 Combine like terms: 0.21 + 0.25 = 0.46 0.25 + 0.125a + a2 = 0.46 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 0.46 Calculate the square root of the right side: 0.678232998 Break this problem into two subproblems by setting (a + 0.5) equal to 0.678232998 and -0.678232998.Subproblem 1
a + 0.5 = 0.678232998 Simplifying a + 0.5 = 0.678232998 Reorder the terms: 0.5 + a = 0.678232998 Solving 0.5 + a = 0.678232998 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 = 0.678232998 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 0.678232998 + -0.5 a = 0.678232998 + -0.5 Combine like terms: 0.678232998 + -0.5 = 0.178232998 a = 0.178232998 Simplifying a = 0.178232998Subproblem 2
a + 0.5 = -0.678232998 Simplifying a + 0.5 = -0.678232998 Reorder the terms: 0.5 + a = -0.678232998 Solving 0.5 + a = -0.678232998 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 = -0.678232998 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -0.678232998 + -0.5 a = -0.678232998 + -0.5 Combine like terms: -0.678232998 + -0.5 = -1.178232998 a = -1.178232998 Simplifying a = -1.178232998Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.178232998, -1.178232998}
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