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Simplifying a2 + -19a + 30 = 0 Reorder the terms: 30 + -19a + a2 = 0 Solving 30 + -19a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -19a + -30 + a2 = 0 + -30 Reorder the terms: 30 + -30 + -19a + a2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -19a + a2 = 0 + -30 -19a + a2 = 0 + -30 Combine like terms: 0 + -30 = -30 -19a + a2 = -30 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 = -30 + 90.25 Reorder the terms: 90.25 + -19a + a2 = -30 + 90.25 Combine like terms: -30 + 90.25 = 60.25 90.25 + -19a + a2 = 60.25 Factor a perfect square on the left side: (a + -9.5)(a + -9.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (a + -9.5) equal to 7.762087348 and -7.762087348.Subproblem 1
a + -9.5 = 7.762087348 Simplifying a + -9.5 = 7.762087348 Reorder the terms: -9.5 + a = 7.762087348 Solving -9.5 + a = 7.762087348 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 = 7.762087348 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + a = 7.762087348 + 9.5 a = 7.762087348 + 9.5 Combine like terms: 7.762087348 + 9.5 = 17.262087348 a = 17.262087348 Simplifying a = 17.262087348Subproblem 2
a + -9.5 = -7.762087348 Simplifying a + -9.5 = -7.762087348 Reorder the terms: -9.5 + a = -7.762087348 Solving -9.5 + a = -7.762087348 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 = -7.762087348 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + a = -7.762087348 + 9.5 a = -7.762087348 + 9.5 Combine like terms: -7.762087348 + 9.5 = 1.737912652 a = 1.737912652 Simplifying a = 1.737912652Solution
The solution to the problem is based on the solutions from the subproblems. a = {17.262087348, 1.737912652}
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