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Simplifying 2a2 + -0.06a + -0.0846 = 0 Reorder the terms: -0.0846 + -0.06a + 2a2 = 0 Solving -0.0846 + -0.06a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.0423 + -0.03a + a2 = 0 Move the constant term to the right: Add '0.0423' to each side of the equation. -0.0423 + -0.03a + 0.0423 + a2 = 0 + 0.0423 Reorder the terms: -0.0423 + 0.0423 + -0.03a + a2 = 0 + 0.0423 Combine like terms: -0.0423 + 0.0423 = 0.0000 0.0000 + -0.03a + a2 = 0 + 0.0423 -0.03a + a2 = 0 + 0.0423 Combine like terms: 0 + 0.0423 = 0.0423 -0.03a + a2 = 0.0423 The a term is -0.03a. Take half its coefficient (-0.015). Square it (0.000225) and add it to both sides. Add '0.000225' to each side of the equation. -0.03a + 0.000225 + a2 = 0.0423 + 0.000225 Reorder the terms: 0.000225 + -0.03a + a2 = 0.0423 + 0.000225 Combine like terms: 0.0423 + 0.000225 = 0.042525 0.000225 + -0.03a + a2 = 0.042525 Factor a perfect square on the left side: (a + -0.015)(a + -0.015) = 0.042525 Calculate the square root of the right side: 0.206215906 Break this problem into two subproblems by setting (a + -0.015) equal to 0.206215906 and -0.206215906.Subproblem 1
a + -0.015 = 0.206215906 Simplifying a + -0.015 = 0.206215906 Reorder the terms: -0.015 + a = 0.206215906 Solving -0.015 + a = 0.206215906 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.015' to each side of the equation. -0.015 + 0.015 + a = 0.206215906 + 0.015 Combine like terms: -0.015 + 0.015 = 0.000 0.000 + a = 0.206215906 + 0.015 a = 0.206215906 + 0.015 Combine like terms: 0.206215906 + 0.015 = 0.221215906 a = 0.221215906 Simplifying a = 0.221215906Subproblem 2
a + -0.015 = -0.206215906 Simplifying a + -0.015 = -0.206215906 Reorder the terms: -0.015 + a = -0.206215906 Solving -0.015 + a = -0.206215906 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.015' to each side of the equation. -0.015 + 0.015 + a = -0.206215906 + 0.015 Combine like terms: -0.015 + 0.015 = 0.000 0.000 + a = -0.206215906 + 0.015 a = -0.206215906 + 0.015 Combine like terms: -0.206215906 + 0.015 = -0.191215906 a = -0.191215906 Simplifying a = -0.191215906Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.221215906, -0.191215906}
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