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Simplifying 3a2 + 18a + -7 = 0 Reorder the terms: -7 + 18a + 3a2 = 0 Solving -7 + 18a + 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'. -2.333333333 + 6a + a2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 6a + 2.333333333 + a2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 6a + a2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 6a + a2 = 0 + 2.333333333 6a + a2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 6a + a2 = 2.333333333 The a term is 6a. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6a + 9 + a2 = 2.333333333 + 9 Reorder the terms: 9 + 6a + a2 = 2.333333333 + 9 Combine like terms: 2.333333333 + 9 = 11.333333333 9 + 6a + a2 = 11.333333333 Factor a perfect square on the left side: (a + 3)(a + 3) = 11.333333333 Calculate the square root of the right side: 3.366501646 Break this problem into two subproblems by setting (a + 3) equal to 3.366501646 and -3.366501646.Subproblem 1
a + 3 = 3.366501646 Simplifying a + 3 = 3.366501646 Reorder the terms: 3 + a = 3.366501646 Solving 3 + a = 3.366501646 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 3.366501646 + -3 Combine like terms: 3 + -3 = 0 0 + a = 3.366501646 + -3 a = 3.366501646 + -3 Combine like terms: 3.366501646 + -3 = 0.366501646 a = 0.366501646 Simplifying a = 0.366501646Subproblem 2
a + 3 = -3.366501646 Simplifying a + 3 = -3.366501646 Reorder the terms: 3 + a = -3.366501646 Solving 3 + a = -3.366501646 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -3.366501646 + -3 Combine like terms: 3 + -3 = 0 0 + a = -3.366501646 + -3 a = -3.366501646 + -3 Combine like terms: -3.366501646 + -3 = -6.366501646 a = -6.366501646 Simplifying a = -6.366501646Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.366501646, -6.366501646}
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