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Simplifying 2a2 + a = 64 Reorder the terms: a + 2a2 = 64 Solving a + 2a2 = 64 Solving for variable 'a'. Reorder the terms: -64 + a + 2a2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -32 + 0.5a + a2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 0.5a + 32 + a2 = 0 + 32 Reorder the terms: -32 + 32 + 0.5a + a2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 0.5a + a2 = 0 + 32 0.5a + a2 = 0 + 32 Combine like terms: 0 + 32 = 32 0.5a + a2 = 32 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. 0.5a + 0.25 + a2 = 32 + 0.25 Reorder the terms: 0.25 + 0.5a + a2 = 32 + 0.25 Combine like terms: 32 + 0.25 = 32.25 0.25 + 0.5a + a2 = 32.25 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (a + 0.5) equal to 5.678908346 and -5.678908346.Subproblem 1
a + 0.5 = 5.678908346 Simplifying a + 0.5 = 5.678908346 Reorder the terms: 0.5 + a = 5.678908346 Solving 0.5 + a = 5.678908346 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 = 5.678908346 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 5.678908346 + -0.5 a = 5.678908346 + -0.5 Combine like terms: 5.678908346 + -0.5 = 5.178908346 a = 5.178908346 Simplifying a = 5.178908346Subproblem 2
a + 0.5 = -5.678908346 Simplifying a + 0.5 = -5.678908346 Reorder the terms: 0.5 + a = -5.678908346 Solving 0.5 + a = -5.678908346 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 = -5.678908346 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -5.678908346 + -0.5 a = -5.678908346 + -0.5 Combine like terms: -5.678908346 + -0.5 = -6.178908346 a = -6.178908346 Simplifying a = -6.178908346Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.178908346, -6.178908346}
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