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Simplifying 4r4 + 15r2 = 4 Reorder the terms: 15r2 + 4r4 = 4 Solving 15r2 + 4r4 = 4 Solving for variable 'r'. Reorder the terms: -4 + 15r2 + 4r4 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 15r2 + 4r4 = 0 Factor a trinomial. (-4 + -1r2)(1 + -4r2) = 0 Factor a difference between two squares. (-4 + -1r2)((1 + 2r)(1 + -2r)) = 0Subproblem 1
Set the factor '(-4 + -1r2)' equal to zero and attempt to solve: Simplifying -4 + -1r2 = 0 Solving -4 + -1r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1r2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1r2 = 0 + 4 -1r2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1r2 = 4 Divide each side by '-1'. r2 = -4 Simplifying r2 = -4 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 + 2r)' equal to zero and attempt to solve: Simplifying 1 + 2r = 0 Solving 1 + 2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2r = 0 + -1 2r = 0 + -1 Combine like terms: 0 + -1 = -1 2r = -1 Divide each side by '2'. r = -0.5 Simplifying r = -0.5Subproblem 3
Set the factor '(1 + -2r)' equal to zero and attempt to solve: Simplifying 1 + -2r = 0 Solving 1 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2r = 0 + -1 -2r = 0 + -1 Combine like terms: 0 + -1 = -1 -2r = -1 Divide each side by '-2'. r = 0.5 Simplifying r = 0.5Solution
r = {-0.5, 0.5}
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