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Simplifying 7a(a + 9) = 104.3 Reorder the terms: 7a(9 + a) = 104.3 (9 * 7a + a * 7a) = 104.3 (63a + 7a2) = 104.3 Solving 63a + 7a2 = 104.3 Solving for variable 'a'. Reorder the terms: -104.3 + 63a + 7a2 = 104.3 + -104.3 Combine like terms: 104.3 + -104.3 = 0.0 -104.3 + 63a + 7a2 = 0.0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -14.9 + 9a + a2 = 0.0 Move the constant term to the right: Add '14.9' to each side of the equation. -14.9 + 9a + 14.9 + a2 = 0.0 + 14.9 Reorder the terms: -14.9 + 14.9 + 9a + a2 = 0.0 + 14.9 Combine like terms: -14.9 + 14.9 = 0.0 0.0 + 9a + a2 = 0.0 + 14.9 9a + a2 = 0.0 + 14.9 Combine like terms: 0.0 + 14.9 = 14.9 9a + a2 = 14.9 The a term is 9a. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9a + 20.25 + a2 = 14.9 + 20.25 Reorder the terms: 20.25 + 9a + a2 = 14.9 + 20.25 Combine like terms: 14.9 + 20.25 = 35.15 20.25 + 9a + a2 = 35.15 Factor a perfect square on the left side: (a + 4.5)(a + 4.5) = 35.15 Calculate the square root of the right side: 5.928743543 Break this problem into two subproblems by setting (a + 4.5) equal to 5.928743543 and -5.928743543.Subproblem 1
a + 4.5 = 5.928743543 Simplifying a + 4.5 = 5.928743543 Reorder the terms: 4.5 + a = 5.928743543 Solving 4.5 + a = 5.928743543 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + a = 5.928743543 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + a = 5.928743543 + -4.5 a = 5.928743543 + -4.5 Combine like terms: 5.928743543 + -4.5 = 1.428743543 a = 1.428743543 Simplifying a = 1.428743543Subproblem 2
a + 4.5 = -5.928743543 Simplifying a + 4.5 = -5.928743543 Reorder the terms: 4.5 + a = -5.928743543 Solving 4.5 + a = -5.928743543 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + a = -5.928743543 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + a = -5.928743543 + -4.5 a = -5.928743543 + -4.5 Combine like terms: -5.928743543 + -4.5 = -10.428743543 a = -10.428743543 Simplifying a = -10.428743543Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.428743543, -10.428743543}
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