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Simplifying 2d4 + -32f4 = 0 Solving 2d4 + -32f4 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '32f4' to each side of the equation. 2d4 + -32f4 + 32f4 = 0 + 32f4 Combine like terms: -32f4 + 32f4 = 0 2d4 + 0 = 0 + 32f4 2d4 = 0 + 32f4 Remove the zero: 2d4 = 32f4 Divide each side by '2'. d4 = 16f4 Simplifying d4 = 16f4 Combine like terms: 16f4 + -16f4 = 0 d4 + -16f4 = 0 Factor a difference between two squares. (d2 + 4f2)(d2 + -4f2) = 0 Factor a difference between two squares. (d2 + 4f2)((d + 2f)(d + -2f)) = 0Subproblem 1
Set the factor '(d2 + 4f2)' equal to zero and attempt to solve: Simplifying d2 + 4f2 = 0 Solving d2 + 4f2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-4f2' to each side of the equation. d2 + 4f2 + -4f2 = 0 + -4f2 Combine like terms: 4f2 + -4f2 = 0 d2 + 0 = 0 + -4f2 d2 = 0 + -4f2 Remove the zero: d2 = -4f2 Simplifying d2 = -4f2 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 '(d + 2f)' equal to zero and attempt to solve: Simplifying d + 2f = 0 Solving d + 2f = 0 Move all terms containing d to the left, all other terms to the right. Add '-2f' to each side of the equation. d + 2f + -2f = 0 + -2f Combine like terms: 2f + -2f = 0 d + 0 = 0 + -2f d = 0 + -2f Remove the zero: d = -2f Simplifying d = -2fSubproblem 3
Set the factor '(d + -2f)' equal to zero and attempt to solve: Simplifying d + -2f = 0 Solving d + -2f = 0 Move all terms containing d to the left, all other terms to the right. Add '2f' to each side of the equation. d + -2f + 2f = 0 + 2f Combine like terms: -2f + 2f = 0 d + 0 = 0 + 2f d = 0 + 2f Remove the zero: d = 2f Simplifying d = 2fSolution
d = {-2f, 2f}
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