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Simplifying a2 + 20a + 88 = 9 Reorder the terms: 88 + 20a + a2 = 9 Solving 88 + 20a + a2 = 9 Solving for variable 'a'. Reorder the terms: 88 + -9 + 20a + a2 = 9 + -9 Combine like terms: 88 + -9 = 79 79 + 20a + a2 = 9 + -9 Combine like terms: 9 + -9 = 0 79 + 20a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-79' to each side of the equation. 79 + 20a + -79 + a2 = 0 + -79 Reorder the terms: 79 + -79 + 20a + a2 = 0 + -79 Combine like terms: 79 + -79 = 0 0 + 20a + a2 = 0 + -79 20a + a2 = 0 + -79 Combine like terms: 0 + -79 = -79 20a + a2 = -79 The a term is 20a. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20a + 100 + a2 = -79 + 100 Reorder the terms: 100 + 20a + a2 = -79 + 100 Combine like terms: -79 + 100 = 21 100 + 20a + a2 = 21 Factor a perfect square on the left side: (a + 10)(a + 10) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (a + 10) equal to 4.582575695 and -4.582575695.Subproblem 1
a + 10 = 4.582575695 Simplifying a + 10 = 4.582575695 Reorder the terms: 10 + a = 4.582575695 Solving 10 + a = 4.582575695 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + a = 4.582575695 + -10 Combine like terms: 10 + -10 = 0 0 + a = 4.582575695 + -10 a = 4.582575695 + -10 Combine like terms: 4.582575695 + -10 = -5.417424305 a = -5.417424305 Simplifying a = -5.417424305Subproblem 2
a + 10 = -4.582575695 Simplifying a + 10 = -4.582575695 Reorder the terms: 10 + a = -4.582575695 Solving 10 + a = -4.582575695 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + a = -4.582575695 + -10 Combine like terms: 10 + -10 = 0 0 + a = -4.582575695 + -10 a = -4.582575695 + -10 Combine like terms: -4.582575695 + -10 = -14.582575695 a = -14.582575695 Simplifying a = -14.582575695Solution
The solution to the problem is based on the solutions from the subproblems. a = {-5.417424305, -14.582575695}
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