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Simplifying 32a4 + -162b4 = 0 Solving 32a4 + -162b4 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '162b4' to each side of the equation. 32a4 + -162b4 + 162b4 = 0 + 162b4 Combine like terms: -162b4 + 162b4 = 0 32a4 + 0 = 0 + 162b4 32a4 = 0 + 162b4 Remove the zero: 32a4 = 162b4 Divide each side by '32'. a4 = 5.0625b4 Simplifying a4 = 5.0625b4 Combine like terms: 5.0625b4 + -5.0625b4 = 0.0000 a4 + -5.0625b4 = 0.0000 Factor a difference between two squares. (a2 + 2.25b2)(a2 + -2.25b2) = 0.0000 Factor a difference between two squares. (a2 + 2.25b2)((a + 1.5b)(a + -1.5b)) = 0.0000Subproblem 1
Set the factor '(a2 + 2.25b2)' equal to zero and attempt to solve: Simplifying a2 + 2.25b2 = 0 Solving a2 + 2.25b2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-2.25b2' to each side of the equation. a2 + 2.25b2 + -2.25b2 = 0 + -2.25b2 Combine like terms: 2.25b2 + -2.25b2 = 0.00 a2 + 0.00 = 0 + -2.25b2 a2 = 0 + -2.25b2 Remove the zero: a2 = -2.25b2 Simplifying a2 = -2.25b2 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 + 1.5b)' equal to zero and attempt to solve: Simplifying a + 1.5b = 0 Solving a + 1.5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1.5b' to each side of the equation. a + 1.5b + -1.5b = 0 + -1.5b Combine like terms: 1.5b + -1.5b = 0.0 a + 0.0 = 0 + -1.5b a = 0 + -1.5b Remove the zero: a = -1.5b Simplifying a = -1.5bSubproblem 3
Set the factor '(a + -1.5b)' equal to zero and attempt to solve: Simplifying a + -1.5b = 0 Solving a + -1.5b = 0 Move all terms containing a to the left, all other terms to the right. Add '1.5b' to each side of the equation. a + -1.5b + 1.5b = 0 + 1.5b Combine like terms: -1.5b + 1.5b = 0.0 a + 0.0 = 0 + 1.5b a = 0 + 1.5b Remove the zero: a = 1.5b Simplifying a = 1.5bSolution
a = {-1.5b, 1.5b}
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