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Simplifying a2 + -18a + -17 = 2a Reorder the terms: -17 + -18a + a2 = 2a Solving -17 + -18a + a2 = 2a Solving for variable 'a'. Reorder the terms: -17 + -18a + -2a + a2 = 2a + -2a Combine like terms: -18a + -2a = -20a -17 + -20a + a2 = 2a + -2a Combine like terms: 2a + -2a = 0 -17 + -20a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -20a + 17 + a2 = 0 + 17 Reorder the terms: -17 + 17 + -20a + a2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -20a + a2 = 0 + 17 -20a + a2 = 0 + 17 Combine like terms: 0 + 17 = 17 -20a + a2 = 17 The a term is -20a. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20a + 100 + a2 = 17 + 100 Reorder the terms: 100 + -20a + a2 = 17 + 100 Combine like terms: 17 + 100 = 117 100 + -20a + a2 = 117 Factor a perfect square on the left side: (a + -10)(a + -10) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (a + -10) equal to 10.816653826 and -10.816653826.Subproblem 1
a + -10 = 10.816653826 Simplifying a + -10 = 10.816653826 Reorder the terms: -10 + a = 10.816653826 Solving -10 + a = 10.816653826 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + a = 10.816653826 + 10 Combine like terms: -10 + 10 = 0 0 + a = 10.816653826 + 10 a = 10.816653826 + 10 Combine like terms: 10.816653826 + 10 = 20.816653826 a = 20.816653826 Simplifying a = 20.816653826Subproblem 2
a + -10 = -10.816653826 Simplifying a + -10 = -10.816653826 Reorder the terms: -10 + a = -10.816653826 Solving -10 + a = -10.816653826 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + a = -10.816653826 + 10 Combine like terms: -10 + 10 = 0 0 + a = -10.816653826 + 10 a = -10.816653826 + 10 Combine like terms: -10.816653826 + 10 = -0.816653826 a = -0.816653826 Simplifying a = -0.816653826Solution
The solution to the problem is based on the solutions from the subproblems. a = {20.816653826, -0.816653826}
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