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Simplifying a2 + -12a + -37 = 0 Reorder the terms: -37 + -12a + a2 = 0 Solving -37 + -12a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -12a + 37 + a2 = 0 + 37 Reorder the terms: -37 + 37 + -12a + a2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -12a + a2 = 0 + 37 -12a + a2 = 0 + 37 Combine like terms: 0 + 37 = 37 -12a + a2 = 37 The a term is -12a. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12a + 36 + a2 = 37 + 36 Reorder the terms: 36 + -12a + a2 = 37 + 36 Combine like terms: 37 + 36 = 73 36 + -12a + a2 = 73 Factor a perfect square on the left side: (a + -6)(a + -6) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (a + -6) equal to 8.544003745 and -8.544003745.Subproblem 1
a + -6 = 8.544003745 Simplifying a + -6 = 8.544003745 Reorder the terms: -6 + a = 8.544003745 Solving -6 + a = 8.544003745 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = 8.544003745 + 6 Combine like terms: -6 + 6 = 0 0 + a = 8.544003745 + 6 a = 8.544003745 + 6 Combine like terms: 8.544003745 + 6 = 14.544003745 a = 14.544003745 Simplifying a = 14.544003745Subproblem 2
a + -6 = -8.544003745 Simplifying a + -6 = -8.544003745 Reorder the terms: -6 + a = -8.544003745 Solving -6 + a = -8.544003745 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = -8.544003745 + 6 Combine like terms: -6 + 6 = 0 0 + a = -8.544003745 + 6 a = -8.544003745 + 6 Combine like terms: -8.544003745 + 6 = -2.544003745 a = -2.544003745 Simplifying a = -2.544003745Solution
The solution to the problem is based on the solutions from the subproblems. a = {14.544003745, -2.544003745}
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