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Simplifying 9a = a2 + -18 Reorder the terms: 9a = -18 + a2 Solving 9a = -18 + a2 Solving for variable 'a'. Reorder the terms: 18 + 9a + -1a2 = -18 + a2 + 18 + -1a2 Reorder the terms: 18 + 9a + -1a2 = -18 + 18 + a2 + -1a2 Combine like terms: -18 + 18 = 0 18 + 9a + -1a2 = 0 + a2 + -1a2 18 + 9a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 18 + 9a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + -9a + a2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -9a + 18 + a2 = 0 + 18 Reorder the terms: -18 + 18 + -9a + a2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -9a + a2 = 0 + 18 -9a + a2 = 0 + 18 Combine like terms: 0 + 18 = 18 -9a + a2 = 18 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 = 18 + 20.25 Reorder the terms: 20.25 + -9a + a2 = 18 + 20.25 Combine like terms: 18 + 20.25 = 38.25 20.25 + -9a + a2 = 38.25 Factor a perfect square on the left side: (a + -4.5)(a + -4.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (a + -4.5) equal to 6.184658438 and -6.184658438.Subproblem 1
a + -4.5 = 6.184658438 Simplifying a + -4.5 = 6.184658438 Reorder the terms: -4.5 + a = 6.184658438 Solving -4.5 + a = 6.184658438 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 = 6.184658438 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 6.184658438 + 4.5 a = 6.184658438 + 4.5 Combine like terms: 6.184658438 + 4.5 = 10.684658438 a = 10.684658438 Simplifying a = 10.684658438Subproblem 2
a + -4.5 = -6.184658438 Simplifying a + -4.5 = -6.184658438 Reorder the terms: -4.5 + a = -6.184658438 Solving -4.5 + a = -6.184658438 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 = -6.184658438 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -6.184658438 + 4.5 a = -6.184658438 + 4.5 Combine like terms: -6.184658438 + 4.5 = -1.684658438 a = -1.684658438 Simplifying a = -1.684658438Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.684658438, -1.684658438}
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