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Simplifying 4r4 + -8r2 = 16 Reorder the terms: -8r2 + 4r4 = 16 Solving -8r2 + 4r4 = 16 Solving for variable 'r'. Reorder the terms: -16 + -8r2 + 4r4 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -8r2 + 4r4 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + -2r2 + r4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -2r2 + r4)' equal to zero and attempt to solve: Simplifying -4 + -2r2 + r4 = 0 Solving -4 + -2r2 + r4 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -2r2 + 4 + r4 = 0 + 4 Reorder the terms: -4 + 4 + -2r2 + r4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2r2 + r4 = 0 + 4 -2r2 + r4 = 0 + 4 Combine like terms: 0 + 4 = 4 -2r2 + r4 = 4 The r term is -2r2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2r2 + 1 + r4 = 4 + 1 Reorder the terms: 1 + -2r2 + r4 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + -2r2 + r4 = 5 Factor a perfect square on the left side: (r2 + -1)(r2 + -1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (r2 + -1) equal to 2.236067978 and -2.236067978.Subproblem 1
r2 + -1 = 2.236067978 Simplifying r2 + -1 = 2.236067978 Reorder the terms: -1 + r2 = 2.236067978 Solving -1 + r2 = 2.236067978 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r2 = 2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + r2 = 2.236067978 + 1 r2 = 2.236067978 + 1 Combine like terms: 2.236067978 + 1 = 3.236067978 r2 = 3.236067978 Simplifying r2 = 3.236067978 Take the square root of each side: r = {-1.79890744, 1.79890744}Subproblem 2
r2 + -1 = -2.236067978 Simplifying r2 + -1 = -2.236067978 Reorder the terms: -1 + r2 = -2.236067978 Solving -1 + r2 = -2.236067978 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r2 = -2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + r2 = -2.236067978 + 1 r2 = -2.236067978 + 1 Combine like terms: -2.236067978 + 1 = -1.236067978 r2 = -1.236067978 Simplifying r2 = -1.236067978 Reorder the terms: 1.236067978 + r2 = -1.236067978 + 1.236067978 Combine like terms: -1.236067978 + 1.236067978 = 0.000000000 1.236067978 + r2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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