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Simplifying -16a + 2a2 + 21 = 0 Reorder the terms: 21 + -16a + 2a2 = 0 Solving 21 + -16a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + -8a + a2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -8a + -10.5 + a2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -8a + a2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -8a + a2 = 0 + -10.5 -8a + a2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -8a + a2 = -10.5 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 = -10.5 + 16 Reorder the terms: 16 + -8a + a2 = -10.5 + 16 Combine like terms: -10.5 + 16 = 5.5 16 + -8a + a2 = 5.5 Factor a perfect square on the left side: (a + -4)(a + -4) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (a + -4) equal to 2.34520788 and -2.34520788.Subproblem 1
a + -4 = 2.34520788 Simplifying a + -4 = 2.34520788 Reorder the terms: -4 + a = 2.34520788 Solving -4 + a = 2.34520788 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 = 2.34520788 + 4 Combine like terms: -4 + 4 = 0 0 + a = 2.34520788 + 4 a = 2.34520788 + 4 Combine like terms: 2.34520788 + 4 = 6.34520788 a = 6.34520788 Simplifying a = 6.34520788Subproblem 2
a + -4 = -2.34520788 Simplifying a + -4 = -2.34520788 Reorder the terms: -4 + a = -2.34520788 Solving -4 + a = -2.34520788 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 = -2.34520788 + 4 Combine like terms: -4 + 4 = 0 0 + a = -2.34520788 + 4 a = -2.34520788 + 4 Combine like terms: -2.34520788 + 4 = 1.65479212 a = 1.65479212 Simplifying a = 1.65479212Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.34520788, 1.65479212}
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