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Simplifying -2a2 + 16a + -18 = 0 Reorder the terms: -18 + 16a + -2a2 = 0 Solving -18 + 16a + -2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 8a + -1a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 8a + -1a2)' equal to zero and attempt to solve: Simplifying -9 + 8a + -1a2 = 0 Solving -9 + 8a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 9 + -8a + a2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -8a + -9 + a2 = 0 + -9 Reorder the terms: 9 + -9 + -8a + a2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8a + a2 = 0 + -9 -8a + a2 = 0 + -9 Combine like terms: 0 + -9 = -9 -8a + a2 = -9 The a term is -8a. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8a + 16 + a2 = -9 + 16 Reorder the terms: 16 + -8a + a2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + -8a + a2 = 7 Factor a perfect square on the left side: (a + -4)(a + -4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (a + -4) equal to 2.645751311 and -2.645751311.Subproblem 1
a + -4 = 2.645751311 Simplifying a + -4 = 2.645751311 Reorder the terms: -4 + a = 2.645751311 Solving -4 + a = 2.645751311 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + a = 2.645751311 + 4 a = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 a = 6.645751311 Simplifying a = 6.645751311Subproblem 2
a + -4 = -2.645751311 Simplifying a + -4 = -2.645751311 Reorder the terms: -4 + a = -2.645751311 Solving -4 + a = -2.645751311 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + a = -2.645751311 + 4 a = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 a = 1.354248689 Simplifying a = 1.354248689Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.645751311, 1.354248689}Solution
a = {6.645751311, 1.354248689}
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