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Simplifying 2a2 + 20a + 50 = 40 Reorder the terms: 50 + 20a + 2a2 = 40 Solving 50 + 20a + 2a2 = 40 Solving for variable 'a'. Reorder the terms: 50 + -40 + 20a + 2a2 = 40 + -40 Combine like terms: 50 + -40 = 10 10 + 20a + 2a2 = 40 + -40 Combine like terms: 40 + -40 = 0 10 + 20a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 10a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 10a + a2)' equal to zero and attempt to solve: Simplifying 5 + 10a + a2 = 0 Solving 5 + 10a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 10a + -5 + a2 = 0 + -5 Reorder the terms: 5 + -5 + 10a + a2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 10a + a2 = 0 + -5 10a + a2 = 0 + -5 Combine like terms: 0 + -5 = -5 10a + a2 = -5 The a term is 10a. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10a + 25 + a2 = -5 + 25 Reorder the terms: 25 + 10a + a2 = -5 + 25 Combine like terms: -5 + 25 = 20 25 + 10a + a2 = 20 Factor a perfect square on the left side: (a + 5)(a + 5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (a + 5) equal to 4.472135955 and -4.472135955.Subproblem 1
a + 5 = 4.472135955 Simplifying a + 5 = 4.472135955 Reorder the terms: 5 + a = 4.472135955 Solving 5 + a = 4.472135955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + a = 4.472135955 + -5 a = 4.472135955 + -5 Combine like terms: 4.472135955 + -5 = -0.527864045 a = -0.527864045 Simplifying a = -0.527864045Subproblem 2
a + 5 = -4.472135955 Simplifying a + 5 = -4.472135955 Reorder the terms: 5 + a = -4.472135955 Solving 5 + a = -4.472135955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = -4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + a = -4.472135955 + -5 a = -4.472135955 + -5 Combine like terms: -4.472135955 + -5 = -9.472135955 a = -9.472135955 Simplifying a = -9.472135955Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.527864045, -9.472135955}Solution
a = {-0.527864045, -9.472135955}
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