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Simplifying 4a2 + 2a + 4a2 + -5 = 0 Reorder the terms: -5 + 2a + 4a2 + 4a2 = 0 Combine like terms: 4a2 + 4a2 = 8a2 -5 + 2a + 8a2 = 0 Solving -5 + 2a + 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'. -0.625 + 0.25a + a2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 0.25a + 0.625 + a2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 0.25a + a2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 0.25a + a2 = 0 + 0.625 0.25a + a2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 0.25a + a2 = 0.625 The a term is 0.25a. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25a + 0.015625 + a2 = 0.625 + 0.015625 Reorder the terms: 0.015625 + 0.25a + a2 = 0.625 + 0.015625 Combine like terms: 0.625 + 0.015625 = 0.640625 0.015625 + 0.25a + a2 = 0.640625 Factor a perfect square on the left side: (a + 0.125)(a + 0.125) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (a + 0.125) equal to 0.80039053 and -0.80039053.Subproblem 1
a + 0.125 = 0.80039053 Simplifying a + 0.125 = 0.80039053 Reorder the terms: 0.125 + a = 0.80039053 Solving 0.125 + a = 0.80039053 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + a = 0.80039053 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + a = 0.80039053 + -0.125 a = 0.80039053 + -0.125 Combine like terms: 0.80039053 + -0.125 = 0.67539053 a = 0.67539053 Simplifying a = 0.67539053Subproblem 2
a + 0.125 = -0.80039053 Simplifying a + 0.125 = -0.80039053 Reorder the terms: 0.125 + a = -0.80039053 Solving 0.125 + a = -0.80039053 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + a = -0.80039053 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + a = -0.80039053 + -0.125 a = -0.80039053 + -0.125 Combine like terms: -0.80039053 + -0.125 = -0.92539053 a = -0.92539053 Simplifying a = -0.92539053Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.67539053, -0.92539053}
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