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Simplifying 3a2 + 6a + -28 = 0 Reorder the terms: -28 + 6a + 3a2 = 0 Solving -28 + 6a + 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'. -9.333333333 + 2a + a2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + 2a + 9.333333333 + a2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + 2a + a2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + 2a + a2 = 0 + 9.333333333 2a + a2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 2a + a2 = 9.333333333 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 9.333333333 + 1 Reorder the terms: 1 + 2a + a2 = 9.333333333 + 1 Combine like terms: 9.333333333 + 1 = 10.333333333 1 + 2a + a2 = 10.333333333 Factor a perfect square on the left side: (a + 1)(a + 1) = 10.333333333 Calculate the square root of the right side: 3.214550254 Break this problem into two subproblems by setting (a + 1) equal to 3.214550254 and -3.214550254.Subproblem 1
a + 1 = 3.214550254 Simplifying a + 1 = 3.214550254 Reorder the terms: 1 + a = 3.214550254 Solving 1 + a = 3.214550254 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 3.214550254 + -1 Combine like terms: 1 + -1 = 0 0 + a = 3.214550254 + -1 a = 3.214550254 + -1 Combine like terms: 3.214550254 + -1 = 2.214550254 a = 2.214550254 Simplifying a = 2.214550254Subproblem 2
a + 1 = -3.214550254 Simplifying a + 1 = -3.214550254 Reorder the terms: 1 + a = -3.214550254 Solving 1 + a = -3.214550254 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -3.214550254 + -1 Combine like terms: 1 + -1 = 0 0 + a = -3.214550254 + -1 a = -3.214550254 + -1 Combine like terms: -3.214550254 + -1 = -4.214550254 a = -4.214550254 Simplifying a = -4.214550254Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.214550254, -4.214550254}
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