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Simplifying b4 + -16a4 = 0 Reorder the terms: -16a4 + b4 = 0 Solving -16a4 + b4 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1b4' to each side of the equation. -16a4 + b4 + -1b4 = 0 + -1b4 Combine like terms: b4 + -1b4 = 0 -16a4 + 0 = 0 + -1b4 -16a4 = 0 + -1b4 Remove the zero: -16a4 = -1b4 Divide each side by '-16'. a4 = 0.0625b4 Simplifying a4 = 0.0625b4 Combine like terms: 0.0625b4 + -0.0625b4 = 0.0000 a4 + -0.0625b4 = 0.0000 Factor a difference between two squares. (a2 + 0.25b2)(a2 + -0.25b2) = 0.0000 Factor a difference between two squares. (a2 + 0.25b2)((a + 0.5b)(a + -0.5b)) = 0.0000Subproblem 1
Set the factor '(a2 + 0.25b2)' equal to zero and attempt to solve: Simplifying a2 + 0.25b2 = 0 Solving a2 + 0.25b2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-0.25b2' to each side of the equation. a2 + 0.25b2 + -0.25b2 = 0 + -0.25b2 Combine like terms: 0.25b2 + -0.25b2 = 0.00 a2 + 0.00 = 0 + -0.25b2 a2 = 0 + -0.25b2 Remove the zero: a2 = -0.25b2 Simplifying a2 = -0.25b2 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 '(a + 0.5b)' equal to zero and attempt to solve: Simplifying a + 0.5b = 0 Solving a + 0.5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-0.5b' to each side of the equation. a + 0.5b + -0.5b = 0 + -0.5b Combine like terms: 0.5b + -0.5b = 0.0 a + 0.0 = 0 + -0.5b a = 0 + -0.5b Remove the zero: a = -0.5b Simplifying a = -0.5bSubproblem 3
Set the factor '(a + -0.5b)' equal to zero and attempt to solve: Simplifying a + -0.5b = 0 Solving a + -0.5b = 0 Move all terms containing a to the left, all other terms to the right. Add '0.5b' to each side of the equation. a + -0.5b + 0.5b = 0 + 0.5b Combine like terms: -0.5b + 0.5b = 0.0 a + 0.0 = 0 + 0.5b a = 0 + 0.5b Remove the zero: a = 0.5b Simplifying a = 0.5bSolution
a = {-0.5b, 0.5b}
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