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Simplifying -21 + -8a = -5a(a + 6) Reorder the terms: -21 + -8a = -5a(6 + a) -21 + -8a = (6 * -5a + a * -5a) -21 + -8a = (-30a + -5a2) Solving -21 + -8a = -30a + -5a2 Solving for variable 'a'. Combine like terms: -8a + 30a = 22a -21 + 22a + 5a2 = -30a + -5a2 + 30a + 5a2 Reorder the terms: -21 + 22a + 5a2 = -30a + 30a + -5a2 + 5a2 Combine like terms: -30a + 30a = 0 -21 + 22a + 5a2 = 0 + -5a2 + 5a2 -21 + 22a + 5a2 = -5a2 + 5a2 Combine like terms: -5a2 + 5a2 = 0 -21 + 22a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + 4.4a + a2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 4.4a + 4.2 + a2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 4.4a + a2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 4.4a + a2 = 0 + 4.2 4.4a + a2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 4.4a + a2 = 4.2 The a term is 4.4a. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4a + 4.84 + a2 = 4.2 + 4.84 Reorder the terms: 4.84 + 4.4a + a2 = 4.2 + 4.84 Combine like terms: 4.2 + 4.84 = 9.04 4.84 + 4.4a + a2 = 9.04 Factor a perfect square on the left side: (a + 2.2)(a + 2.2) = 9.04 Calculate the square root of the right side: 3.006659276 Break this problem into two subproblems by setting (a + 2.2) equal to 3.006659276 and -3.006659276.Subproblem 1
a + 2.2 = 3.006659276 Simplifying a + 2.2 = 3.006659276 Reorder the terms: 2.2 + a = 3.006659276 Solving 2.2 + a = 3.006659276 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + a = 3.006659276 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + a = 3.006659276 + -2.2 a = 3.006659276 + -2.2 Combine like terms: 3.006659276 + -2.2 = 0.806659276 a = 0.806659276 Simplifying a = 0.806659276Subproblem 2
a + 2.2 = -3.006659276 Simplifying a + 2.2 = -3.006659276 Reorder the terms: 2.2 + a = -3.006659276 Solving 2.2 + a = -3.006659276 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + a = -3.006659276 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + a = -3.006659276 + -2.2 a = -3.006659276 + -2.2 Combine like terms: -3.006659276 + -2.2 = -5.206659276 a = -5.206659276 Simplifying a = -5.206659276Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.806659276, -5.206659276}
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