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Simplifying 0.03383a2 + a + -640.44 = 0 Reorder the terms: -640.44 + a + 0.03383a2 = 0 Solving -640.44 + a + 0.03383a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 0.03383 the coefficient of the squared term: Divide each side by '0.03383'. -18931.12622 + 29.55956252a + a2 = 0 Move the constant term to the right: Add '18931.12622' to each side of the equation. -18931.12622 + 29.55956252a + 18931.12622 + a2 = 0 + 18931.12622 Reorder the terms: -18931.12622 + 18931.12622 + 29.55956252a + a2 = 0 + 18931.12622 Combine like terms: -18931.12622 + 18931.12622 = 0.00000 0.00000 + 29.55956252a + a2 = 0 + 18931.12622 29.55956252a + a2 = 0 + 18931.12622 Combine like terms: 0 + 18931.12622 = 18931.12622 29.55956252a + a2 = 18931.12622 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. 29.55956252a + 0.25 + a2 = 18931.12622 + 0.25 Reorder the terms: 0.25 + 29.55956252a + a2 = 18931.12622 + 0.25 Combine like terms: 18931.12622 + 0.25 = 18931.37622 0.25 + 29.55956252a + a2 = 18931.37622 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 18931.37622 Calculate the square root of the right side: 137.591337736 Break this problem into two subproblems by setting (a + 0.5) equal to 137.591337736 and -137.591337736.Subproblem 1
a + 0.5 = 137.591337736 Simplifying a + 0.5 = 137.591337736 Reorder the terms: 0.5 + a = 137.591337736 Solving 0.5 + a = 137.591337736 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 = 137.591337736 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 137.591337736 + -0.5 a = 137.591337736 + -0.5 Combine like terms: 137.591337736 + -0.5 = 137.091337736 a = 137.091337736 Simplifying a = 137.091337736Subproblem 2
a + 0.5 = -137.591337736 Simplifying a + 0.5 = -137.591337736 Reorder the terms: 0.5 + a = -137.591337736 Solving 0.5 + a = -137.591337736 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 = -137.591337736 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -137.591337736 + -0.5 a = -137.591337736 + -0.5 Combine like terms: -137.591337736 + -0.5 = -138.091337736 a = -138.091337736 Simplifying a = -138.091337736Solution
The solution to the problem is based on the solutions from the subproblems. a = {137.091337736, -138.091337736}
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