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Simplifying a8 + -4a7 = 4a6 Reorder the terms: -4a7 + a8 = 4a6 Solving -4a7 + a8 = 4a6 Solving for variable 'a'. Reorder the terms: -4a6 + -4a7 + a8 = 4a6 + -4a6 Combine like terms: 4a6 + -4a6 = 0 -4a6 + -4a7 + a8 = 0 Factor out the Greatest Common Factor (GCF), 'a6'. a6(-4 + -4a + a2) = 0Subproblem 1
Set the factor 'a6' equal to zero and attempt to solve: Simplifying a6 = 0 Solving a6 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a6 = 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 '(-4 + -4a + a2)' equal to zero and attempt to solve: Simplifying -4 + -4a + a2 = 0 Solving -4 + -4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -4a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + -4a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4a + a2 = 0 + 4 -4a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4a + a2 = 4 The a term is -4a. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4a + 4 + a2 = 4 + 4 Reorder the terms: 4 + -4a + a2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + -4a + a2 = 8 Factor a perfect square on the left side: (a + -2)(a + -2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (a + -2) equal to 2.828427125 and -2.828427125.Subproblem 1
a + -2 = 2.828427125 Simplifying a + -2 = 2.828427125 Reorder the terms: -2 + a = 2.828427125 Solving -2 + a = 2.828427125 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + a = 2.828427125 + 2 a = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 a = 4.828427125 Simplifying a = 4.828427125Subproblem 2
a + -2 = -2.828427125 Simplifying a + -2 = -2.828427125 Reorder the terms: -2 + a = -2.828427125 Solving -2 + a = -2.828427125 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + a = -2.828427125 + 2 a = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 a = -0.828427125 Simplifying a = -0.828427125Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.828427125, -0.828427125}Solution
a = {4.828427125, -0.828427125}
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