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Simplifying a2 + -14a + -44 = 0 Reorder the terms: -44 + -14a + a2 = 0 Solving -44 + -14a + 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 + -14a + 44 + a2 = 0 + 44 Reorder the terms: -44 + 44 + -14a + a2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -14a + a2 = 0 + 44 -14a + a2 = 0 + 44 Combine like terms: 0 + 44 = 44 -14a + a2 = 44 The a term is -14a. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14a + 49 + a2 = 44 + 49 Reorder the terms: 49 + -14a + a2 = 44 + 49 Combine like terms: 44 + 49 = 93 49 + -14a + a2 = 93 Factor a perfect square on the left side: (a + -7)(a + -7) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (a + -7) equal to 9.643650761 and -9.643650761.Subproblem 1
a + -7 = 9.643650761 Simplifying a + -7 = 9.643650761 Reorder the terms: -7 + a = 9.643650761 Solving -7 + a = 9.643650761 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = 9.643650761 + 7 Combine like terms: -7 + 7 = 0 0 + a = 9.643650761 + 7 a = 9.643650761 + 7 Combine like terms: 9.643650761 + 7 = 16.643650761 a = 16.643650761 Simplifying a = 16.643650761Subproblem 2
a + -7 = -9.643650761 Simplifying a + -7 = -9.643650761 Reorder the terms: -7 + a = -9.643650761 Solving -7 + a = -9.643650761 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = -9.643650761 + 7 Combine like terms: -7 + 7 = 0 0 + a = -9.643650761 + 7 a = -9.643650761 + 7 Combine like terms: -9.643650761 + 7 = -2.643650761 a = -2.643650761 Simplifying a = -2.643650761Solution
The solution to the problem is based on the solutions from the subproblems. a = {16.643650761, -2.643650761}
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