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Simplifying a2 + 16a + -22 = 0 Reorder the terms: -22 + 16a + a2 = 0 Solving -22 + 16a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 16a + 22 + a2 = 0 + 22 Reorder the terms: -22 + 22 + 16a + a2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 16a + a2 = 0 + 22 16a + a2 = 0 + 22 Combine like terms: 0 + 22 = 22 16a + a2 = 22 The a term is 16a. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16a + 64 + a2 = 22 + 64 Reorder the terms: 64 + 16a + a2 = 22 + 64 Combine like terms: 22 + 64 = 86 64 + 16a + a2 = 86 Factor a perfect square on the left side: (a + 8)(a + 8) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (a + 8) equal to 9.273618495 and -9.273618495.Subproblem 1
a + 8 = 9.273618495 Simplifying a + 8 = 9.273618495 Reorder the terms: 8 + a = 9.273618495 Solving 8 + a = 9.273618495 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = 9.273618495 + -8 Combine like terms: 8 + -8 = 0 0 + a = 9.273618495 + -8 a = 9.273618495 + -8 Combine like terms: 9.273618495 + -8 = 1.273618495 a = 1.273618495 Simplifying a = 1.273618495Subproblem 2
a + 8 = -9.273618495 Simplifying a + 8 = -9.273618495 Reorder the terms: 8 + a = -9.273618495 Solving 8 + a = -9.273618495 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = -9.273618495 + -8 Combine like terms: 8 + -8 = 0 0 + a = -9.273618495 + -8 a = -9.273618495 + -8 Combine like terms: -9.273618495 + -8 = -17.273618495 a = -17.273618495 Simplifying a = -17.273618495Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.273618495, -17.273618495}
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