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Simplifying 4a2 + -1a + -6 = 0 Reorder the terms: -6 + -1a + 4a2 = 0 Solving -6 + -1a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + -0.25a + a2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.25a + 1.5 + a2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.25a + a2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.25a + a2 = 0 + 1.5 -0.25a + a2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -0.25a + a2 = 1.5 The a term is -0.25a. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25a + 0.015625 + a2 = 1.5 + 0.015625 Reorder the terms: 0.015625 + -0.25a + a2 = 1.5 + 0.015625 Combine like terms: 1.5 + 0.015625 = 1.515625 0.015625 + -0.25a + a2 = 1.515625 Factor a perfect square on the left side: (a + -0.125)(a + -0.125) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (a + -0.125) equal to 1.231107225 and -1.231107225.Subproblem 1
a + -0.125 = 1.231107225 Simplifying a + -0.125 = 1.231107225 Reorder the terms: -0.125 + a = 1.231107225 Solving -0.125 + a = 1.231107225 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + a = 1.231107225 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + a = 1.231107225 + 0.125 a = 1.231107225 + 0.125 Combine like terms: 1.231107225 + 0.125 = 1.356107225 a = 1.356107225 Simplifying a = 1.356107225Subproblem 2
a + -0.125 = -1.231107225 Simplifying a + -0.125 = -1.231107225 Reorder the terms: -0.125 + a = -1.231107225 Solving -0.125 + a = -1.231107225 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + a = -1.231107225 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + a = -1.231107225 + 0.125 a = -1.231107225 + 0.125 Combine like terms: -1.231107225 + 0.125 = -1.106107225 a = -1.106107225 Simplifying a = -1.106107225Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.356107225, -1.106107225}
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