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Simplifying (2a + -6)(2a + 1) = a Reorder the terms: (-6 + 2a)(2a + 1) = a Reorder the terms: (-6 + 2a)(1 + 2a) = a Multiply (-6 + 2a) * (1 + 2a) (-6(1 + 2a) + 2a * (1 + 2a)) = a ((1 * -6 + 2a * -6) + 2a * (1 + 2a)) = a ((-6 + -12a) + 2a * (1 + 2a)) = a (-6 + -12a + (1 * 2a + 2a * 2a)) = a (-6 + -12a + (2a + 4a2)) = a Combine like terms: -12a + 2a = -10a (-6 + -10a + 4a2) = a Solving -6 + -10a + 4a2 = a Solving for variable 'a'. Reorder the terms: -6 + -10a + -1a + 4a2 = a + -1a Combine like terms: -10a + -1a = -11a -6 + -11a + 4a2 = a + -1a Combine like terms: a + -1a = 0 -6 + -11a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + -2.75a + a2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.75a + 1.5 + a2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.75a + a2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.75a + a2 = 0 + 1.5 -2.75a + a2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.75a + a2 = 1.5 The a term is -2.75a. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75a + 1.890625 + a2 = 1.5 + 1.890625 Reorder the terms: 1.890625 + -2.75a + a2 = 1.5 + 1.890625 Combine like terms: 1.5 + 1.890625 = 3.390625 1.890625 + -2.75a + a2 = 3.390625 Factor a perfect square on the left side: (a + -1.375)(a + -1.375) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting (a + -1.375) equal to 1.841364983 and -1.841364983.Subproblem 1
a + -1.375 = 1.841364983 Simplifying a + -1.375 = 1.841364983 Reorder the terms: -1.375 + a = 1.841364983 Solving -1.375 + a = 1.841364983 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + a = 1.841364983 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + a = 1.841364983 + 1.375 a = 1.841364983 + 1.375 Combine like terms: 1.841364983 + 1.375 = 3.216364983 a = 3.216364983 Simplifying a = 3.216364983Subproblem 2
a + -1.375 = -1.841364983 Simplifying a + -1.375 = -1.841364983 Reorder the terms: -1.375 + a = -1.841364983 Solving -1.375 + a = -1.841364983 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + a = -1.841364983 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + a = -1.841364983 + 1.375 a = -1.841364983 + 1.375 Combine like terms: -1.841364983 + 1.375 = -0.466364983 a = -0.466364983 Simplifying a = -0.466364983Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.216364983, -0.466364983}
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