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Simplifying 30 + 8a = -5a(a + 7) Reorder the terms: 30 + 8a = -5a(7 + a) 30 + 8a = (7 * -5a + a * -5a) 30 + 8a = (-35a + -5a2) Solving 30 + 8a = -35a + -5a2 Solving for variable 'a'. Combine like terms: 8a + 35a = 43a 30 + 43a + 5a2 = -35a + -5a2 + 35a + 5a2 Reorder the terms: 30 + 43a + 5a2 = -35a + 35a + -5a2 + 5a2 Combine like terms: -35a + 35a = 0 30 + 43a + 5a2 = 0 + -5a2 + 5a2 30 + 43a + 5a2 = -5a2 + 5a2 Combine like terms: -5a2 + 5a2 = 0 30 + 43a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6 + 8.6a + a2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 8.6a + -6 + a2 = 0 + -6 Reorder the terms: 6 + -6 + 8.6a + a2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 8.6a + a2 = 0 + -6 8.6a + a2 = 0 + -6 Combine like terms: 0 + -6 = -6 8.6a + a2 = -6 The a term is 8.6a. Take half its coefficient (4.3). Square it (18.49) and add it to both sides. Add '18.49' to each side of the equation. 8.6a + 18.49 + a2 = -6 + 18.49 Reorder the terms: 18.49 + 8.6a + a2 = -6 + 18.49 Combine like terms: -6 + 18.49 = 12.49 18.49 + 8.6a + a2 = 12.49 Factor a perfect square on the left side: (a + 4.3)(a + 4.3) = 12.49 Calculate the square root of the right side: 3.534119409 Break this problem into two subproblems by setting (a + 4.3) equal to 3.534119409 and -3.534119409.Subproblem 1
a + 4.3 = 3.534119409 Simplifying a + 4.3 = 3.534119409 Reorder the terms: 4.3 + a = 3.534119409 Solving 4.3 + a = 3.534119409 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.3' to each side of the equation. 4.3 + -4.3 + a = 3.534119409 + -4.3 Combine like terms: 4.3 + -4.3 = 0.0 0.0 + a = 3.534119409 + -4.3 a = 3.534119409 + -4.3 Combine like terms: 3.534119409 + -4.3 = -0.765880591 a = -0.765880591 Simplifying a = -0.765880591Subproblem 2
a + 4.3 = -3.534119409 Simplifying a + 4.3 = -3.534119409 Reorder the terms: 4.3 + a = -3.534119409 Solving 4.3 + a = -3.534119409 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.3' to each side of the equation. 4.3 + -4.3 + a = -3.534119409 + -4.3 Combine like terms: 4.3 + -4.3 = 0.0 0.0 + a = -3.534119409 + -4.3 a = -3.534119409 + -4.3 Combine like terms: -3.534119409 + -4.3 = -7.834119409 a = -7.834119409 Simplifying a = -7.834119409Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.765880591, -7.834119409}
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