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Simplifying 25a2 + -7a2 + -18a + -4 + -6a + 9a2 = 0 Reorder the terms: -4 + -18a + -6a + 25a2 + -7a2 + 9a2 = 0 Combine like terms: -18a + -6a = -24a -4 + -24a + 25a2 + -7a2 + 9a2 = 0 Combine like terms: 25a2 + -7a2 = 18a2 -4 + -24a + 18a2 + 9a2 = 0 Combine like terms: 18a2 + 9a2 = 27a2 -4 + -24a + 27a2 = 0 Solving -4 + -24a + 27a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.1481481481 + -0.8888888889a + a2 = 0 Move the constant term to the right: Add '0.1481481481' to each side of the equation. -0.1481481481 + -0.8888888889a + 0.1481481481 + a2 = 0 + 0.1481481481 Reorder the terms: -0.1481481481 + 0.1481481481 + -0.8888888889a + a2 = 0 + 0.1481481481 Combine like terms: -0.1481481481 + 0.1481481481 = 0.0000000000 0.0000000000 + -0.8888888889a + a2 = 0 + 0.1481481481 -0.8888888889a + a2 = 0 + 0.1481481481 Combine like terms: 0 + 0.1481481481 = 0.1481481481 -0.8888888889a + a2 = 0.1481481481 The a term is -0.8888888889a. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889a + 0.1975308642 + a2 = 0.1481481481 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889a + a2 = 0.1481481481 + 0.1975308642 Combine like terms: 0.1481481481 + 0.1975308642 = 0.3456790123 0.1975308642 + -0.8888888889a + a2 = 0.3456790123 Factor a perfect square on the left side: (a + -0.4444444445)(a + -0.4444444445) = 0.3456790123 Calculate the square root of the right side: 0.587944736 Break this problem into two subproblems by setting (a + -0.4444444445) equal to 0.587944736 and -0.587944736.Subproblem 1
a + -0.4444444445 = 0.587944736 Simplifying a + -0.4444444445 = 0.587944736 Reorder the terms: -0.4444444445 + a = 0.587944736 Solving -0.4444444445 + a = 0.587944736 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + a = 0.587944736 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + a = 0.587944736 + 0.4444444445 a = 0.587944736 + 0.4444444445 Combine like terms: 0.587944736 + 0.4444444445 = 1.0323891805 a = 1.0323891805 Simplifying a = 1.0323891805Subproblem 2
a + -0.4444444445 = -0.587944736 Simplifying a + -0.4444444445 = -0.587944736 Reorder the terms: -0.4444444445 + a = -0.587944736 Solving -0.4444444445 + a = -0.587944736 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + a = -0.587944736 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + a = -0.587944736 + 0.4444444445 a = -0.587944736 + 0.4444444445 Combine like terms: -0.587944736 + 0.4444444445 = -0.1435002915 a = -0.1435002915 Simplifying a = -0.1435002915Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.0323891805, -0.1435002915}
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