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Simplifying 5a2 + a = 2 Reorder the terms: a + 5a2 = 2 Solving a + 5a2 = 2 Solving for variable 'a'. Reorder the terms: -2 + a + 5a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 0.2a + a2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.2a + 0.4 + a2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.2a + a2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.2a + a2 = 0 + 0.4 0.2a + a2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.2a + a2 = 0.4 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. 0.2a + 0.25 + a2 = 0.4 + 0.25 Reorder the terms: 0.25 + 0.2a + a2 = 0.4 + 0.25 Combine like terms: 0.4 + 0.25 = 0.65 0.25 + 0.2a + a2 = 0.65 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 0.65 Calculate the square root of the right side: 0.806225775 Break this problem into two subproblems by setting (a + 0.5) equal to 0.806225775 and -0.806225775.Subproblem 1
a + 0.5 = 0.806225775 Simplifying a + 0.5 = 0.806225775 Reorder the terms: 0.5 + a = 0.806225775 Solving 0.5 + a = 0.806225775 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 = 0.806225775 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 0.806225775 + -0.5 a = 0.806225775 + -0.5 Combine like terms: 0.806225775 + -0.5 = 0.306225775 a = 0.306225775 Simplifying a = 0.306225775Subproblem 2
a + 0.5 = -0.806225775 Simplifying a + 0.5 = -0.806225775 Reorder the terms: 0.5 + a = -0.806225775 Solving 0.5 + a = -0.806225775 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 = -0.806225775 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -0.806225775 + -0.5 a = -0.806225775 + -0.5 Combine like terms: -0.806225775 + -0.5 = -1.306225775 a = -1.306225775 Simplifying a = -1.306225775Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.306225775, -1.306225775}
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