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Simplifying a2 + -9a + -63 = 0 Reorder the terms: -63 + -9a + a2 = 0 Solving -63 + -9a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + -9a + 63 + a2 = 0 + 63 Reorder the terms: -63 + 63 + -9a + a2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -9a + a2 = 0 + 63 -9a + a2 = 0 + 63 Combine like terms: 0 + 63 = 63 -9a + a2 = 63 The a term is -9a. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9a + 20.25 + a2 = 63 + 20.25 Reorder the terms: 20.25 + -9a + a2 = 63 + 20.25 Combine like terms: 63 + 20.25 = 83.25 20.25 + -9a + a2 = 83.25 Factor a perfect square on the left side: (a + -4.5)(a + -4.5) = 83.25 Calculate the square root of the right side: 9.124143795 Break this problem into two subproblems by setting (a + -4.5) equal to 9.124143795 and -9.124143795.Subproblem 1
a + -4.5 = 9.124143795 Simplifying a + -4.5 = 9.124143795 Reorder the terms: -4.5 + a = 9.124143795 Solving -4.5 + a = 9.124143795 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + a = 9.124143795 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 9.124143795 + 4.5 a = 9.124143795 + 4.5 Combine like terms: 9.124143795 + 4.5 = 13.624143795 a = 13.624143795 Simplifying a = 13.624143795Subproblem 2
a + -4.5 = -9.124143795 Simplifying a + -4.5 = -9.124143795 Reorder the terms: -4.5 + a = -9.124143795 Solving -4.5 + a = -9.124143795 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + a = -9.124143795 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -9.124143795 + 4.5 a = -9.124143795 + 4.5 Combine like terms: -9.124143795 + 4.5 = -4.624143795 a = -4.624143795 Simplifying a = -4.624143795Solution
The solution to the problem is based on the solutions from the subproblems. a = {13.624143795, -4.624143795}
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