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Simplifying 10a2 + -5a + -2 = 0 Reorder the terms: -2 + -5a + 10a2 = 0 Solving -2 + -5a + 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'. -0.2 + -0.5a + a2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.5a + 0.2 + a2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.5a + a2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.5a + a2 = 0 + 0.2 -0.5a + a2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.5a + a2 = 0.2 The a term is -0.5a. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5a + 0.0625 + a2 = 0.2 + 0.0625 Reorder the terms: 0.0625 + -0.5a + a2 = 0.2 + 0.0625 Combine like terms: 0.2 + 0.0625 = 0.2625 0.0625 + -0.5a + a2 = 0.2625 Factor a perfect square on the left side: (a + -0.25)(a + -0.25) = 0.2625 Calculate the square root of the right side: 0.512347538 Break this problem into two subproblems by setting (a + -0.25) equal to 0.512347538 and -0.512347538.Subproblem 1
a + -0.25 = 0.512347538 Simplifying a + -0.25 = 0.512347538 Reorder the terms: -0.25 + a = 0.512347538 Solving -0.25 + a = 0.512347538 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = 0.512347538 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 0.512347538 + 0.25 a = 0.512347538 + 0.25 Combine like terms: 0.512347538 + 0.25 = 0.762347538 a = 0.762347538 Simplifying a = 0.762347538Subproblem 2
a + -0.25 = -0.512347538 Simplifying a + -0.25 = -0.512347538 Reorder the terms: -0.25 + a = -0.512347538 Solving -0.25 + a = -0.512347538 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = -0.512347538 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -0.512347538 + 0.25 a = -0.512347538 + 0.25 Combine like terms: -0.512347538 + 0.25 = -0.262347538 a = -0.262347538 Simplifying a = -0.262347538Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.762347538, -0.262347538}
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