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Simplifying 2a2 + 16a + -13 = 0 Reorder the terms: -13 + 16a + 2a2 = 0 Solving -13 + 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'. -6.5 + 8a + a2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 8a + 6.5 + a2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 8a + a2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 8a + a2 = 0 + 6.5 8a + a2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 8a + a2 = 6.5 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 = 6.5 + 16 Reorder the terms: 16 + 8a + a2 = 6.5 + 16 Combine like terms: 6.5 + 16 = 22.5 16 + 8a + a2 = 22.5 Factor a perfect square on the left side: (a + 4)(a + 4) = 22.5 Calculate the square root of the right side: 4.74341649 Break this problem into two subproblems by setting (a + 4) equal to 4.74341649 and -4.74341649.Subproblem 1
a + 4 = 4.74341649 Simplifying a + 4 = 4.74341649 Reorder the terms: 4 + a = 4.74341649 Solving 4 + a = 4.74341649 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 = 4.74341649 + -4 Combine like terms: 4 + -4 = 0 0 + a = 4.74341649 + -4 a = 4.74341649 + -4 Combine like terms: 4.74341649 + -4 = 0.74341649 a = 0.74341649 Simplifying a = 0.74341649Subproblem 2
a + 4 = -4.74341649 Simplifying a + 4 = -4.74341649 Reorder the terms: 4 + a = -4.74341649 Solving 4 + a = -4.74341649 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 = -4.74341649 + -4 Combine like terms: 4 + -4 = 0 0 + a = -4.74341649 + -4 a = -4.74341649 + -4 Combine like terms: -4.74341649 + -4 = -8.74341649 a = -8.74341649 Simplifying a = -8.74341649Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.74341649, -8.74341649}
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