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Simplifying a2 + 8a = 192 * 8 Reorder the terms: 8a + a2 = 192 * 8 Multiply 192 * 8 8a + a2 = 1536 Solving 8a + a2 = 1536 Solving for variable 'a'. Reorder the terms: -1536 + 8a + a2 = 1536 + -1536 Combine like terms: 1536 + -1536 = 0 -1536 + 8a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '1536' to each side of the equation. -1536 + 8a + 1536 + a2 = 0 + 1536 Reorder the terms: -1536 + 1536 + 8a + a2 = 0 + 1536 Combine like terms: -1536 + 1536 = 0 0 + 8a + a2 = 0 + 1536 8a + a2 = 0 + 1536 Combine like terms: 0 + 1536 = 1536 8a + a2 = 1536 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 = 1536 + 16 Reorder the terms: 16 + 8a + a2 = 1536 + 16 Combine like terms: 1536 + 16 = 1552 16 + 8a + a2 = 1552 Factor a perfect square on the left side: (a + 4)(a + 4) = 1552 Calculate the square root of the right side: 39.395431207 Break this problem into two subproblems by setting (a + 4) equal to 39.395431207 and -39.395431207.Subproblem 1
a + 4 = 39.395431207 Simplifying a + 4 = 39.395431207 Reorder the terms: 4 + a = 39.395431207 Solving 4 + a = 39.395431207 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 = 39.395431207 + -4 Combine like terms: 4 + -4 = 0 0 + a = 39.395431207 + -4 a = 39.395431207 + -4 Combine like terms: 39.395431207 + -4 = 35.395431207 a = 35.395431207 Simplifying a = 35.395431207Subproblem 2
a + 4 = -39.395431207 Simplifying a + 4 = -39.395431207 Reorder the terms: 4 + a = -39.395431207 Solving 4 + a = -39.395431207 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 = -39.395431207 + -4 Combine like terms: 4 + -4 = 0 0 + a = -39.395431207 + -4 a = -39.395431207 + -4 Combine like terms: -39.395431207 + -4 = -43.395431207 a = -43.395431207 Simplifying a = -43.395431207Solution
The solution to the problem is based on the solutions from the subproblems. a = {35.395431207, -43.395431207}
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