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Simplifying 2a4 + 21a3 + 4a2 = 0 Reorder the terms: 4a2 + 21a3 + 2a4 = 0 Solving 4a2 + 21a3 + 2a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a2'. a2(4 + 21a + 2a2) = 0Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve: Simplifying a2 = 0 Solving a2 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a2 = 0 Take the square root of each side: a = {0}Subproblem 2
Set the factor '(4 + 21a + 2a2)' equal to zero and attempt to solve: Simplifying 4 + 21a + 2a2 = 0 Solving 4 + 21a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 10.5a + a2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 10.5a + -2 + a2 = 0 + -2 Reorder the terms: 2 + -2 + 10.5a + a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 10.5a + a2 = 0 + -2 10.5a + a2 = 0 + -2 Combine like terms: 0 + -2 = -2 10.5a + a2 = -2 The a term is 10.5a. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5a + 27.5625 + a2 = -2 + 27.5625 Reorder the terms: 27.5625 + 10.5a + a2 = -2 + 27.5625 Combine like terms: -2 + 27.5625 = 25.5625 27.5625 + 10.5a + a2 = 25.5625 Factor a perfect square on the left side: (a + 5.25)(a + 5.25) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (a + 5.25) equal to 5.055937104 and -5.055937104.Subproblem 1
a + 5.25 = 5.055937104 Simplifying a + 5.25 = 5.055937104 Reorder the terms: 5.25 + a = 5.055937104 Solving 5.25 + a = 5.055937104 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + a = 5.055937104 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + a = 5.055937104 + -5.25 a = 5.055937104 + -5.25 Combine like terms: 5.055937104 + -5.25 = -0.194062896 a = -0.194062896 Simplifying a = -0.194062896Subproblem 2
a + 5.25 = -5.055937104 Simplifying a + 5.25 = -5.055937104 Reorder the terms: 5.25 + a = -5.055937104 Solving 5.25 + a = -5.055937104 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + a = -5.055937104 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + a = -5.055937104 + -5.25 a = -5.055937104 + -5.25 Combine like terms: -5.055937104 + -5.25 = -10.305937104 a = -10.305937104 Simplifying a = -10.305937104Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.194062896, -10.305937104}Solution
a = {0, -0.194062896, -10.305937104}
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