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Simplifying 2a2 + 19a + 28 = 0 Reorder the terms: 28 + 19a + 2a2 = 0 Solving 28 + 19a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14 + 9.5a + a2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + 9.5a + -14 + a2 = 0 + -14 Reorder the terms: 14 + -14 + 9.5a + a2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 9.5a + a2 = 0 + -14 9.5a + a2 = 0 + -14 Combine like terms: 0 + -14 = -14 9.5a + a2 = -14 The a term is 9.5a. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5a + 22.5625 + a2 = -14 + 22.5625 Reorder the terms: 22.5625 + 9.5a + a2 = -14 + 22.5625 Combine like terms: -14 + 22.5625 = 8.5625 22.5625 + 9.5a + a2 = 8.5625 Factor a perfect square on the left side: (a + 4.75)(a + 4.75) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (a + 4.75) equal to 2.926174978 and -2.926174978.Subproblem 1
a + 4.75 = 2.926174978 Simplifying a + 4.75 = 2.926174978 Reorder the terms: 4.75 + a = 2.926174978 Solving 4.75 + a = 2.926174978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + a = 2.926174978 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + a = 2.926174978 + -4.75 a = 2.926174978 + -4.75 Combine like terms: 2.926174978 + -4.75 = -1.823825022 a = -1.823825022 Simplifying a = -1.823825022Subproblem 2
a + 4.75 = -2.926174978 Simplifying a + 4.75 = -2.926174978 Reorder the terms: 4.75 + a = -2.926174978 Solving 4.75 + a = -2.926174978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + a = -2.926174978 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + a = -2.926174978 + -4.75 a = -2.926174978 + -4.75 Combine like terms: -2.926174978 + -4.75 = -7.676174978 a = -7.676174978 Simplifying a = -7.676174978Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.823825022, -7.676174978}
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