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Simplifying 9a2 = -8a + 10 Reorder the terms: 9a2 = 10 + -8a Solving 9a2 = 10 + -8a Solving for variable 'a'. Reorder the terms: -10 + 8a + 9a2 = 10 + -8a + -10 + 8a Reorder the terms: -10 + 8a + 9a2 = 10 + -10 + -8a + 8a Combine like terms: 10 + -10 = 0 -10 + 8a + 9a2 = 0 + -8a + 8a -10 + 8a + 9a2 = -8a + 8a Combine like terms: -8a + 8a = 0 -10 + 8a + 9a2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + 0.8888888889a + a2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 0.8888888889a + 1.111111111 + a2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 0.8888888889a + a2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 0.8888888889a + a2 = 0 + 1.111111111 0.8888888889a + a2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 0.8888888889a + a2 = 1.111111111 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 = 1.111111111 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889a + a2 = 1.111111111 + 0.1975308642 Combine like terms: 1.111111111 + 0.1975308642 = 1.3086419752 0.1975308642 + 0.8888888889a + a2 = 1.3086419752 Factor a perfect square on the left side: (a + 0.4444444445)(a + 0.4444444445) = 1.3086419752 Calculate the square root of the right side: 1.143958905 Break this problem into two subproblems by setting (a + 0.4444444445) equal to 1.143958905 and -1.143958905.Subproblem 1
a + 0.4444444445 = 1.143958905 Simplifying a + 0.4444444445 = 1.143958905 Reorder the terms: 0.4444444445 + a = 1.143958905 Solving 0.4444444445 + a = 1.143958905 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 = 1.143958905 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + a = 1.143958905 + -0.4444444445 a = 1.143958905 + -0.4444444445 Combine like terms: 1.143958905 + -0.4444444445 = 0.6995144605 a = 0.6995144605 Simplifying a = 0.6995144605Subproblem 2
a + 0.4444444445 = -1.143958905 Simplifying a + 0.4444444445 = -1.143958905 Reorder the terms: 0.4444444445 + a = -1.143958905 Solving 0.4444444445 + a = -1.143958905 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 = -1.143958905 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + a = -1.143958905 + -0.4444444445 a = -1.143958905 + -0.4444444445 Combine like terms: -1.143958905 + -0.4444444445 = -1.5884033495 a = -1.5884033495 Simplifying a = -1.5884033495Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.6995144605, -1.5884033495}
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