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Simplifying a2 + 20a = -2 Reorder the terms: 20a + a2 = -2 Solving 20a + a2 = -2 Solving for variable 'a'. Reorder the terms: 2 + 20a + a2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 20a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 20a + -2 + a2 = 0 + -2 Reorder the terms: 2 + -2 + 20a + a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 20a + a2 = 0 + -2 20a + a2 = 0 + -2 Combine like terms: 0 + -2 = -2 20a + a2 = -2 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 = -2 + 100 Reorder the terms: 100 + 20a + a2 = -2 + 100 Combine like terms: -2 + 100 = 98 100 + 20a + a2 = 98 Factor a perfect square on the left side: (a + 10)(a + 10) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (a + 10) equal to 9.899494937 and -9.899494937.Subproblem 1
a + 10 = 9.899494937 Simplifying a + 10 = 9.899494937 Reorder the terms: 10 + a = 9.899494937 Solving 10 + a = 9.899494937 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 = 9.899494937 + -10 Combine like terms: 10 + -10 = 0 0 + a = 9.899494937 + -10 a = 9.899494937 + -10 Combine like terms: 9.899494937 + -10 = -0.100505063 a = -0.100505063 Simplifying a = -0.100505063Subproblem 2
a + 10 = -9.899494937 Simplifying a + 10 = -9.899494937 Reorder the terms: 10 + a = -9.899494937 Solving 10 + a = -9.899494937 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 = -9.899494937 + -10 Combine like terms: 10 + -10 = 0 0 + a = -9.899494937 + -10 a = -9.899494937 + -10 Combine like terms: -9.899494937 + -10 = -19.899494937 a = -19.899494937 Simplifying a = -19.899494937Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.100505063, -19.899494937}
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