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Simplifying 216 = 3a2 + -12a Reorder the terms: 216 = -12a + 3a2 Solving 216 = -12a + 3a2 Solving for variable 'a'. Reorder the terms: 216 + 12a + -3a2 = -12a + 12a + 3a2 + -3a2 Combine like terms: -12a + 12a = 0 216 + 12a + -3a2 = 0 + 3a2 + -3a2 216 + 12a + -3a2 = 3a2 + -3a2 Combine like terms: 3a2 + -3a2 = 0 216 + 12a + -3a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(72 + 4a + -1a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(72 + 4a + -1a2)' equal to zero and attempt to solve: Simplifying 72 + 4a + -1a2 = 0 Solving 72 + 4a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -72 + -4a + a2 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + -4a + 72 + a2 = 0 + 72 Reorder the terms: -72 + 72 + -4a + a2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -4a + a2 = 0 + 72 -4a + a2 = 0 + 72 Combine like terms: 0 + 72 = 72 -4a + a2 = 72 The a term is -4a. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4a + 4 + a2 = 72 + 4 Reorder the terms: 4 + -4a + a2 = 72 + 4 Combine like terms: 72 + 4 = 76 4 + -4a + a2 = 76 Factor a perfect square on the left side: (a + -2)(a + -2) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (a + -2) equal to 8.717797887 and -8.717797887.Subproblem 1
a + -2 = 8.717797887 Simplifying a + -2 = 8.717797887 Reorder the terms: -2 + a = 8.717797887 Solving -2 + a = 8.717797887 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 8.717797887 + 2 Combine like terms: -2 + 2 = 0 0 + a = 8.717797887 + 2 a = 8.717797887 + 2 Combine like terms: 8.717797887 + 2 = 10.717797887 a = 10.717797887 Simplifying a = 10.717797887Subproblem 2
a + -2 = -8.717797887 Simplifying a + -2 = -8.717797887 Reorder the terms: -2 + a = -8.717797887 Solving -2 + a = -8.717797887 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = -8.717797887 + 2 Combine like terms: -2 + 2 = 0 0 + a = -8.717797887 + 2 a = -8.717797887 + 2 Combine like terms: -8.717797887 + 2 = -6.717797887 a = -6.717797887 Simplifying a = -6.717797887Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.717797887, -6.717797887}Solution
a = {10.717797887, -6.717797887}
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