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Simplifying -10a2 + -1a + 8 = 0 Reorder the terms: 8 + -1a + -10a2 = 0 Solving 8 + -1a + -10a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.8 + 0.1a + a2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.1a + 0.8 + a2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.1a + a2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.1a + a2 = 0 + 0.8 0.1a + a2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.1a + a2 = 0.8 The a term is 0.1a. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1a + 0.0025 + a2 = 0.8 + 0.0025 Reorder the terms: 0.0025 + 0.1a + a2 = 0.8 + 0.0025 Combine like terms: 0.8 + 0.0025 = 0.8025 0.0025 + 0.1a + a2 = 0.8025 Factor a perfect square on the left side: (a + 0.05)(a + 0.05) = 0.8025 Calculate the square root of the right side: 0.895823643 Break this problem into two subproblems by setting (a + 0.05) equal to 0.895823643 and -0.895823643.Subproblem 1
a + 0.05 = 0.895823643 Simplifying a + 0.05 = 0.895823643 Reorder the terms: 0.05 + a = 0.895823643 Solving 0.05 + a = 0.895823643 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + a = 0.895823643 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + a = 0.895823643 + -0.05 a = 0.895823643 + -0.05 Combine like terms: 0.895823643 + -0.05 = 0.845823643 a = 0.845823643 Simplifying a = 0.845823643Subproblem 2
a + 0.05 = -0.895823643 Simplifying a + 0.05 = -0.895823643 Reorder the terms: 0.05 + a = -0.895823643 Solving 0.05 + a = -0.895823643 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + a = -0.895823643 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + a = -0.895823643 + -0.05 a = -0.895823643 + -0.05 Combine like terms: -0.895823643 + -0.05 = -0.945823643 a = -0.945823643 Simplifying a = -0.945823643Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.845823643, -0.945823643}
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