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Simplifying 0 = a2 + -9a + 12 Reorder the terms: 0 = 12 + -9a + a2 Solving 0 = 12 + -9a + a2 Solving for variable 'a'. Combine like terms: 0 + -12 = -12 -12 + 9a + -1a2 = 12 + -9a + a2 + -12 + 9a + -1a2 Reorder the terms: -12 + 9a + -1a2 = 12 + -12 + -9a + 9a + a2 + -1a2 Combine like terms: 12 + -12 = 0 -12 + 9a + -1a2 = 0 + -9a + 9a + a2 + -1a2 -12 + 9a + -1a2 = -9a + 9a + a2 + -1a2 Combine like terms: -9a + 9a = 0 -12 + 9a + -1a2 = 0 + a2 + -1a2 -12 + 9a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 -12 + 9a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -9a + a2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -9a + -12 + a2 = 0 + -12 Reorder the terms: 12 + -12 + -9a + a2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -9a + a2 = 0 + -12 -9a + a2 = 0 + -12 Combine like terms: 0 + -12 = -12 -9a + a2 = -12 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 = -12 + 20.25 Reorder the terms: 20.25 + -9a + a2 = -12 + 20.25 Combine like terms: -12 + 20.25 = 8.25 20.25 + -9a + a2 = 8.25 Factor a perfect square on the left side: (a + -4.5)(a + -4.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (a + -4.5) equal to 2.872281323 and -2.872281323.Subproblem 1
a + -4.5 = 2.872281323 Simplifying a + -4.5 = 2.872281323 Reorder the terms: -4.5 + a = 2.872281323 Solving -4.5 + a = 2.872281323 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 = 2.872281323 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 2.872281323 + 4.5 a = 2.872281323 + 4.5 Combine like terms: 2.872281323 + 4.5 = 7.372281323 a = 7.372281323 Simplifying a = 7.372281323Subproblem 2
a + -4.5 = -2.872281323 Simplifying a + -4.5 = -2.872281323 Reorder the terms: -4.5 + a = -2.872281323 Solving -4.5 + a = -2.872281323 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 = -2.872281323 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -2.872281323 + 4.5 a = -2.872281323 + 4.5 Combine like terms: -2.872281323 + 4.5 = 1.627718677 a = 1.627718677 Simplifying a = 1.627718677Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.372281323, 1.627718677}
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