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Simplifying 4a2b2 + -20ab2 + 20b2 = 0 Reorder the terms: -20ab2 + 4a2b2 + 20b2 = 0 Solving -20ab2 + 4a2b2 + 20b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4b2'. 4b2(-5a + a2 + 5) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'b2' equal to zero and attempt to solve: Simplifying b2 = 0 Solving b2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b2' to each side of the equation. b2 + -1b2 = 0 + -1b2 Remove the zero: 0 = -1b2 Simplifying 0 = -1b2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-5a + a2 + 5)' equal to zero and attempt to solve: Simplifying -5a + a2 + 5 = 0 Reorder the terms: 5 + -5a + a2 = 0 Solving 5 + -5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -5a + -5 + a2 = 0 + -5 Reorder the terms: 5 + -5 + -5a + a2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5a + a2 = 0 + -5 -5a + a2 = 0 + -5 Combine like terms: 0 + -5 = -5 -5a + a2 = -5 The a term is -5a. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5a + 6.25 + a2 = -5 + 6.25 Reorder the terms: 6.25 + -5a + a2 = -5 + 6.25 Combine like terms: -5 + 6.25 = 1.25 6.25 + -5a + a2 = 1.25 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (a + -2.5) equal to 1.118033989 and -1.118033989.Subproblem 1
a + -2.5 = 1.118033989 Simplifying a + -2.5 = 1.118033989 Reorder the terms: -2.5 + a = 1.118033989 Solving -2.5 + a = 1.118033989 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 1.118033989 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 1.118033989 + 2.5 a = 1.118033989 + 2.5 Combine like terms: 1.118033989 + 2.5 = 3.618033989 a = 3.618033989 Simplifying a = 3.618033989Subproblem 2
a + -2.5 = -1.118033989 Simplifying a + -2.5 = -1.118033989 Reorder the terms: -2.5 + a = -1.118033989 Solving -2.5 + a = -1.118033989 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -1.118033989 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -1.118033989 + 2.5 a = -1.118033989 + 2.5 Combine like terms: -1.118033989 + 2.5 = 1.381966011 a = 1.381966011 Simplifying a = 1.381966011Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.618033989, 1.381966011}Solution
a = {3.618033989, 1.381966011}
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