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Simplifying 7a4 + -35a3 + -14a2 = 0 Reorder the terms: -14a2 + -35a3 + 7a4 = 0 Solving -14a2 + -35a3 + 7a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '7a2'. 7a2(-2 + -5a + a2) = 0 Ignore the factor 7.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 '(-2 + -5a + a2)' equal to zero and attempt to solve: Simplifying -2 + -5a + a2 = 0 Solving -2 + -5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -5a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + -5a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5a + a2 = 0 + 2 -5a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -5a + a2 = 2 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 = 2 + 6.25 Reorder the terms: 6.25 + -5a + a2 = 2 + 6.25 Combine like terms: 2 + 6.25 = 8.25 6.25 + -5a + a2 = 8.25 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (a + -2.5) equal to 2.872281323 and -2.872281323.Subproblem 1
a + -2.5 = 2.872281323 Simplifying a + -2.5 = 2.872281323 Reorder the terms: -2.5 + a = 2.872281323 Solving -2.5 + a = 2.872281323 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 = 2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 2.872281323 + 2.5 a = 2.872281323 + 2.5 Combine like terms: 2.872281323 + 2.5 = 5.372281323 a = 5.372281323 Simplifying a = 5.372281323Subproblem 2
a + -2.5 = -2.872281323 Simplifying a + -2.5 = -2.872281323 Reorder the terms: -2.5 + a = -2.872281323 Solving -2.5 + a = -2.872281323 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 = -2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -2.872281323 + 2.5 a = -2.872281323 + 2.5 Combine like terms: -2.872281323 + 2.5 = -0.372281323 a = -0.372281323 Simplifying a = -0.372281323Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.372281323, -0.372281323}Solution
a = {0, 5.372281323, -0.372281323}
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