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Simplifying a2 + -5a + -44 = 0 Reorder the terms: -44 + -5a + a2 = 0 Solving -44 + -5a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -5a + 44 + a2 = 0 + 44 Reorder the terms: -44 + 44 + -5a + a2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -5a + a2 = 0 + 44 -5a + a2 = 0 + 44 Combine like terms: 0 + 44 = 44 -5a + a2 = 44 The a term is -5a. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5a + 6.25 + a2 = 44 + 6.25 Reorder the terms: 6.25 + -5a + a2 = 44 + 6.25 Combine like terms: 44 + 6.25 = 50.25 6.25 + -5a + a2 = 50.25 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (a + -2.5) equal to 7.088723439 and -7.088723439.Subproblem 1
a + -2.5 = 7.088723439 Simplifying a + -2.5 = 7.088723439 Reorder the terms: -2.5 + a = 7.088723439 Solving -2.5 + a = 7.088723439 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 7.088723439 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 7.088723439 + 2.5 a = 7.088723439 + 2.5 Combine like terms: 7.088723439 + 2.5 = 9.588723439 a = 9.588723439 Simplifying a = 9.588723439Subproblem 2
a + -2.5 = -7.088723439 Simplifying a + -2.5 = -7.088723439 Reorder the terms: -2.5 + a = -7.088723439 Solving -2.5 + a = -7.088723439 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -7.088723439 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -7.088723439 + 2.5 a = -7.088723439 + 2.5 Combine like terms: -7.088723439 + 2.5 = -4.588723439 a = -4.588723439 Simplifying a = -4.588723439Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.588723439, -4.588723439}
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