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Simplifying a2 + 17a + -88 = 0 Reorder the terms: -88 + 17a + a2 = 0 Solving -88 + 17a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 17a + 88 + a2 = 0 + 88 Reorder the terms: -88 + 88 + 17a + a2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 17a + a2 = 0 + 88 17a + a2 = 0 + 88 Combine like terms: 0 + 88 = 88 17a + a2 = 88 The a term is 17a. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17a + 72.25 + a2 = 88 + 72.25 Reorder the terms: 72.25 + 17a + a2 = 88 + 72.25 Combine like terms: 88 + 72.25 = 160.25 72.25 + 17a + a2 = 160.25 Factor a perfect square on the left side: (a + 8.5)(a + 8.5) = 160.25 Calculate the square root of the right side: 12.658988901 Break this problem into two subproblems by setting (a + 8.5) equal to 12.658988901 and -12.658988901.Subproblem 1
a + 8.5 = 12.658988901 Simplifying a + 8.5 = 12.658988901 Reorder the terms: 8.5 + a = 12.658988901 Solving 8.5 + a = 12.658988901 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + a = 12.658988901 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + a = 12.658988901 + -8.5 a = 12.658988901 + -8.5 Combine like terms: 12.658988901 + -8.5 = 4.158988901 a = 4.158988901 Simplifying a = 4.158988901Subproblem 2
a + 8.5 = -12.658988901 Simplifying a + 8.5 = -12.658988901 Reorder the terms: 8.5 + a = -12.658988901 Solving 8.5 + a = -12.658988901 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + a = -12.658988901 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + a = -12.658988901 + -8.5 a = -12.658988901 + -8.5 Combine like terms: -12.658988901 + -8.5 = -21.158988901 a = -21.158988901 Simplifying a = -21.158988901Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.158988901, -21.158988901}
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