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Simplifying a2 + -14a = 24 Reorder the terms: -14a + a2 = 24 Solving -14a + a2 = 24 Solving for variable 'a'. Reorder the terms: -24 + -14a + a2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -14a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -14a + 24 + a2 = 0 + 24 Reorder the terms: -24 + 24 + -14a + a2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -14a + a2 = 0 + 24 -14a + a2 = 0 + 24 Combine like terms: 0 + 24 = 24 -14a + a2 = 24 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 = 24 + 49 Reorder the terms: 49 + -14a + a2 = 24 + 49 Combine like terms: 24 + 49 = 73 49 + -14a + a2 = 73 Factor a perfect square on the left side: (a + -7)(a + -7) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (a + -7) equal to 8.544003745 and -8.544003745.Subproblem 1
a + -7 = 8.544003745 Simplifying a + -7 = 8.544003745 Reorder the terms: -7 + a = 8.544003745 Solving -7 + a = 8.544003745 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 = 8.544003745 + 7 Combine like terms: -7 + 7 = 0 0 + a = 8.544003745 + 7 a = 8.544003745 + 7 Combine like terms: 8.544003745 + 7 = 15.544003745 a = 15.544003745 Simplifying a = 15.544003745Subproblem 2
a + -7 = -8.544003745 Simplifying a + -7 = -8.544003745 Reorder the terms: -7 + a = -8.544003745 Solving -7 + a = -8.544003745 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 = -8.544003745 + 7 Combine like terms: -7 + 7 = 0 0 + a = -8.544003745 + 7 a = -8.544003745 + 7 Combine like terms: -8.544003745 + 7 = -1.544003745 a = -1.544003745 Simplifying a = -1.544003745Solution
The solution to the problem is based on the solutions from the subproblems. a = {15.544003745, -1.544003745}
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