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Simplifying 64a2 + 12a2 + 44a + 5 = 0 Reorder the terms: 5 + 44a + 64a2 + 12a2 = 0 Combine like terms: 64a2 + 12a2 = 76a2 5 + 44a + 76a2 = 0 Solving 5 + 44a + 76a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 76 the coefficient of the squared term: Divide each side by '76'. 0.06578947368 + 0.5789473684a + a2 = 0 Move the constant term to the right: Add '-0.06578947368' to each side of the equation. 0.06578947368 + 0.5789473684a + -0.06578947368 + a2 = 0 + -0.06578947368 Reorder the terms: 0.06578947368 + -0.06578947368 + 0.5789473684a + a2 = 0 + -0.06578947368 Combine like terms: 0.06578947368 + -0.06578947368 = 0.00000000000 0.00000000000 + 0.5789473684a + a2 = 0 + -0.06578947368 0.5789473684a + a2 = 0 + -0.06578947368 Combine like terms: 0 + -0.06578947368 = -0.06578947368 0.5789473684a + a2 = -0.06578947368 The a term is 0.5789473684a. Take half its coefficient (0.2894736842). Square it (0.08379501384) and add it to both sides. Add '0.08379501384' to each side of the equation. 0.5789473684a + 0.08379501384 + a2 = -0.06578947368 + 0.08379501384 Reorder the terms: 0.08379501384 + 0.5789473684a + a2 = -0.06578947368 + 0.08379501384 Combine like terms: -0.06578947368 + 0.08379501384 = 0.01800554016 0.08379501384 + 0.5789473684a + a2 = 0.01800554016 Factor a perfect square on the left side: (a + 0.2894736842)(a + 0.2894736842) = 0.01800554016 Calculate the square root of the right side: 0.134184724 Break this problem into two subproblems by setting (a + 0.2894736842) equal to 0.134184724 and -0.134184724.Subproblem 1
a + 0.2894736842 = 0.134184724 Simplifying a + 0.2894736842 = 0.134184724 Reorder the terms: 0.2894736842 + a = 0.134184724 Solving 0.2894736842 + a = 0.134184724 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2894736842' to each side of the equation. 0.2894736842 + -0.2894736842 + a = 0.134184724 + -0.2894736842 Combine like terms: 0.2894736842 + -0.2894736842 = 0.0000000000 0.0000000000 + a = 0.134184724 + -0.2894736842 a = 0.134184724 + -0.2894736842 Combine like terms: 0.134184724 + -0.2894736842 = -0.1552889602 a = -0.1552889602 Simplifying a = -0.1552889602Subproblem 2
a + 0.2894736842 = -0.134184724 Simplifying a + 0.2894736842 = -0.134184724 Reorder the terms: 0.2894736842 + a = -0.134184724 Solving 0.2894736842 + a = -0.134184724 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2894736842' to each side of the equation. 0.2894736842 + -0.2894736842 + a = -0.134184724 + -0.2894736842 Combine like terms: 0.2894736842 + -0.2894736842 = 0.0000000000 0.0000000000 + a = -0.134184724 + -0.2894736842 a = -0.134184724 + -0.2894736842 Combine like terms: -0.134184724 + -0.2894736842 = -0.4236584082 a = -0.4236584082 Simplifying a = -0.4236584082Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.1552889602, -0.4236584082}
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