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Simplifying 4a4 = 2 + -7a2 Solving 4a4 = 2 + -7a2 Solving for variable 'a'. Reorder the terms: -2 + 7a2 + 4a4 = 2 + -7a2 + -2 + 7a2 Reorder the terms: -2 + 7a2 + 4a4 = 2 + -2 + -7a2 + 7a2 Combine like terms: 2 + -2 = 0 -2 + 7a2 + 4a4 = 0 + -7a2 + 7a2 -2 + 7a2 + 4a4 = -7a2 + 7a2 Combine like terms: -7a2 + 7a2 = 0 -2 + 7a2 + 4a4 = 0 Factor a trinomial. (-2 + -1a2)(1 + -4a2) = 0 Factor a difference between two squares. (-2 + -1a2)((1 + 2a)(1 + -2a)) = 0Subproblem 1
Set the factor '(-2 + -1a2)' equal to zero and attempt to solve: Simplifying -2 + -1a2 = 0 Solving -2 + -1a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1a2 = 0 + 2 -1a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1a2 = 2 Divide each side by '-1'. a2 = -2 Simplifying a2 = -2 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 '(1 + 2a)' equal to zero and attempt to solve: Simplifying 1 + 2a = 0 Solving 1 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2a = 0 + -1 2a = 0 + -1 Combine like terms: 0 + -1 = -1 2a = -1 Divide each side by '2'. a = -0.5 Simplifying a = -0.5Subproblem 3
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Solution
a = {-0.5, 0.5}
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