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Simplifying 28a5 + 35a4 + -70a3 = 0 Reorder the terms: -70a3 + 35a4 + 28a5 = 0 Solving -70a3 + 35a4 + 28a5 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '7a3'. 7a3(-10 + 5a + 4a2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'a3' equal to zero and attempt to solve: Simplifying a3 = 0 Solving a3 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a3 = 0 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 '(-10 + 5a + 4a2)' equal to zero and attempt to solve: Simplifying -10 + 5a + 4a2 = 0 Solving -10 + 5a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5 + 1.25a + a2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 1.25a + 2.5 + a2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 1.25a + a2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 1.25a + a2 = 0 + 2.5 1.25a + a2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 1.25a + a2 = 2.5 The a term is 1.25a. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25a + 0.390625 + a2 = 2.5 + 0.390625 Reorder the terms: 0.390625 + 1.25a + a2 = 2.5 + 0.390625 Combine like terms: 2.5 + 0.390625 = 2.890625 0.390625 + 1.25a + a2 = 2.890625 Factor a perfect square on the left side: (a + 0.625)(a + 0.625) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (a + 0.625) equal to 1.700183814 and -1.700183814.Subproblem 1
a + 0.625 = 1.700183814 Simplifying a + 0.625 = 1.700183814 Reorder the terms: 0.625 + a = 1.700183814 Solving 0.625 + a = 1.700183814 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + a = 1.700183814 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + a = 1.700183814 + -0.625 a = 1.700183814 + -0.625 Combine like terms: 1.700183814 + -0.625 = 1.075183814 a = 1.075183814 Simplifying a = 1.075183814Subproblem 2
a + 0.625 = -1.700183814 Simplifying a + 0.625 = -1.700183814 Reorder the terms: 0.625 + a = -1.700183814 Solving 0.625 + a = -1.700183814 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + a = -1.700183814 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + a = -1.700183814 + -0.625 a = -1.700183814 + -0.625 Combine like terms: -1.700183814 + -0.625 = -2.325183814 a = -2.325183814 Simplifying a = -2.325183814Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.075183814, -2.325183814}Solution
a = {1.075183814, -2.325183814}
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