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Simplifying 2a2(5a2 + 2a + -4) = 0 Reorder the terms: 2a2(-4 + 2a + 5a2) = 0 (-4 * 2a2 + 2a * 2a2 + 5a2 * 2a2) = 0 (-8a2 + 4a3 + 10a4) = 0 Solving -8a2 + 4a3 + 10a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a2'. 2a2(-4 + 2a + 5a2) = 0 Ignore the factor 2.Subproblem 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 + 2a + 5a2)' equal to zero and attempt to solve: Simplifying -4 + 2a + 5a2 = 0 Solving -4 + 2a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 0.4a + a2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.4a + 0.8 + a2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.4a + a2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.4a + a2 = 0 + 0.8 0.4a + a2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.4a + a2 = 0.8 The a term is 0.4a. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4a + 0.04 + a2 = 0.8 + 0.04 Reorder the terms: 0.04 + 0.4a + a2 = 0.8 + 0.04 Combine like terms: 0.8 + 0.04 = 0.84 0.04 + 0.4a + a2 = 0.84 Factor a perfect square on the left side: (a + 0.2)(a + 0.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (a + 0.2) equal to 0.916515139 and -0.916515139.Subproblem 1
a + 0.2 = 0.916515139 Simplifying a + 0.2 = 0.916515139 Reorder the terms: 0.2 + a = 0.916515139 Solving 0.2 + a = 0.916515139 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + a = 0.916515139 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + a = 0.916515139 + -0.2 a = 0.916515139 + -0.2 Combine like terms: 0.916515139 + -0.2 = 0.716515139 a = 0.716515139 Simplifying a = 0.716515139Subproblem 2
a + 0.2 = -0.916515139 Simplifying a + 0.2 = -0.916515139 Reorder the terms: 0.2 + a = -0.916515139 Solving 0.2 + a = -0.916515139 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + a = -0.916515139 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + a = -0.916515139 + -0.2 a = -0.916515139 + -0.2 Combine like terms: -0.916515139 + -0.2 = -1.116515139 a = -1.116515139 Simplifying a = -1.116515139Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.716515139, -1.116515139}Solution
a = {0, 0.716515139, -1.116515139}
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