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Simplifying -1a2 + -28a + 192 = 0 Reorder the terms: 192 + -28a + -1a2 = 0 Solving 192 + -28a + -1a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -192 + 28a + a2 = 0 Move the constant term to the right: Add '192' to each side of the equation. -192 + 28a + 192 + a2 = 0 + 192 Reorder the terms: -192 + 192 + 28a + a2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 28a + a2 = 0 + 192 28a + a2 = 0 + 192 Combine like terms: 0 + 192 = 192 28a + a2 = 192 The a term is 28a. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28a + 196 + a2 = 192 + 196 Reorder the terms: 196 + 28a + a2 = 192 + 196 Combine like terms: 192 + 196 = 388 196 + 28a + a2 = 388 Factor a perfect square on the left side: (a + 14)(a + 14) = 388 Calculate the square root of the right side: 19.697715604 Break this problem into two subproblems by setting (a + 14) equal to 19.697715604 and -19.697715604.Subproblem 1
a + 14 = 19.697715604 Simplifying a + 14 = 19.697715604 Reorder the terms: 14 + a = 19.697715604 Solving 14 + a = 19.697715604 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + a = 19.697715604 + -14 Combine like terms: 14 + -14 = 0 0 + a = 19.697715604 + -14 a = 19.697715604 + -14 Combine like terms: 19.697715604 + -14 = 5.697715604 a = 5.697715604 Simplifying a = 5.697715604Subproblem 2
a + 14 = -19.697715604 Simplifying a + 14 = -19.697715604 Reorder the terms: 14 + a = -19.697715604 Solving 14 + a = -19.697715604 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + a = -19.697715604 + -14 Combine like terms: 14 + -14 = 0 0 + a = -19.697715604 + -14 a = -19.697715604 + -14 Combine like terms: -19.697715604 + -14 = -33.697715604 a = -33.697715604 Simplifying a = -33.697715604Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.697715604, -33.697715604}
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