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Simplifying a2 + 19a + -1 = 0 Reorder the terms: -1 + 19a + a2 = 0 Solving -1 + 19a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 19a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + 19a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 19a + a2 = 0 + 1 19a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 19a + a2 = 1 The a term is 19a. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19a + 90.25 + a2 = 1 + 90.25 Reorder the terms: 90.25 + 19a + a2 = 1 + 90.25 Combine like terms: 1 + 90.25 = 91.25 90.25 + 19a + a2 = 91.25 Factor a perfect square on the left side: (a + 9.5)(a + 9.5) = 91.25 Calculate the square root of the right side: 9.552486587 Break this problem into two subproblems by setting (a + 9.5) equal to 9.552486587 and -9.552486587.Subproblem 1
a + 9.5 = 9.552486587 Simplifying a + 9.5 = 9.552486587 Reorder the terms: 9.5 + a = 9.552486587 Solving 9.5 + a = 9.552486587 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + a = 9.552486587 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + a = 9.552486587 + -9.5 a = 9.552486587 + -9.5 Combine like terms: 9.552486587 + -9.5 = 0.052486587 a = 0.052486587 Simplifying a = 0.052486587Subproblem 2
a + 9.5 = -9.552486587 Simplifying a + 9.5 = -9.552486587 Reorder the terms: 9.5 + a = -9.552486587 Solving 9.5 + a = -9.552486587 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + a = -9.552486587 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + a = -9.552486587 + -9.5 a = -9.552486587 + -9.5 Combine like terms: -9.552486587 + -9.5 = -19.052486587 a = -19.052486587 Simplifying a = -19.052486587Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.052486587, -19.052486587}
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