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Simplifying a2 + -40a + 218 = 0 Reorder the terms: 218 + -40a + a2 = 0 Solving 218 + -40a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-218' to each side of the equation. 218 + -40a + -218 + a2 = 0 + -218 Reorder the terms: 218 + -218 + -40a + a2 = 0 + -218 Combine like terms: 218 + -218 = 0 0 + -40a + a2 = 0 + -218 -40a + a2 = 0 + -218 Combine like terms: 0 + -218 = -218 -40a + a2 = -218 The a term is -40a. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40a + 400 + a2 = -218 + 400 Reorder the terms: 400 + -40a + a2 = -218 + 400 Combine like terms: -218 + 400 = 182 400 + -40a + a2 = 182 Factor a perfect square on the left side: (a + -20)(a + -20) = 182 Calculate the square root of the right side: 13.490737563 Break this problem into two subproblems by setting (a + -20) equal to 13.490737563 and -13.490737563.Subproblem 1
a + -20 = 13.490737563 Simplifying a + -20 = 13.490737563 Reorder the terms: -20 + a = 13.490737563 Solving -20 + a = 13.490737563 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + a = 13.490737563 + 20 Combine like terms: -20 + 20 = 0 0 + a = 13.490737563 + 20 a = 13.490737563 + 20 Combine like terms: 13.490737563 + 20 = 33.490737563 a = 33.490737563 Simplifying a = 33.490737563Subproblem 2
a + -20 = -13.490737563 Simplifying a + -20 = -13.490737563 Reorder the terms: -20 + a = -13.490737563 Solving -20 + a = -13.490737563 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + a = -13.490737563 + 20 Combine like terms: -20 + 20 = 0 0 + a = -13.490737563 + 20 a = -13.490737563 + 20 Combine like terms: -13.490737563 + 20 = 6.509262437 a = 6.509262437 Simplifying a = 6.509262437Solution
The solution to the problem is based on the solutions from the subproblems. a = {33.490737563, 6.509262437}
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