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Simplifying 3a2 + 36a + 10 = 0 Reorder the terms: 10 + 36a + 3a2 = 0 Solving 10 + 36a + 3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + 12a + a2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + 12a + -3.333333333 + a2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + 12a + a2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + 12a + a2 = 0 + -3.333333333 12a + a2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 12a + a2 = -3.333333333 The a term is 12a. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12a + 36 + a2 = -3.333333333 + 36 Reorder the terms: 36 + 12a + a2 = -3.333333333 + 36 Combine like terms: -3.333333333 + 36 = 32.666666667 36 + 12a + a2 = 32.666666667 Factor a perfect square on the left side: (a + 6)(a + 6) = 32.666666667 Calculate the square root of the right side: 5.715476067 Break this problem into two subproblems by setting (a + 6) equal to 5.715476067 and -5.715476067.Subproblem 1
a + 6 = 5.715476067 Simplifying a + 6 = 5.715476067 Reorder the terms: 6 + a = 5.715476067 Solving 6 + a = 5.715476067 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = 5.715476067 + -6 Combine like terms: 6 + -6 = 0 0 + a = 5.715476067 + -6 a = 5.715476067 + -6 Combine like terms: 5.715476067 + -6 = -0.284523933 a = -0.284523933 Simplifying a = -0.284523933Subproblem 2
a + 6 = -5.715476067 Simplifying a + 6 = -5.715476067 Reorder the terms: 6 + a = -5.715476067 Solving 6 + a = -5.715476067 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = -5.715476067 + -6 Combine like terms: 6 + -6 = 0 0 + a = -5.715476067 + -6 a = -5.715476067 + -6 Combine like terms: -5.715476067 + -6 = -11.715476067 a = -11.715476067 Simplifying a = -11.715476067Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.284523933, -11.715476067}
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