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Simplifying 2r4 + 46r2 + -100 = 0 Reorder the terms: -100 + 46r2 + 2r4 = 0 Solving -100 + 46r2 + 2r4 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 23r2 + r4) = 0 Factor a trinomial. 2((-25 + -1r2)(2 + -1r2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -1r2)' equal to zero and attempt to solve: Simplifying -25 + -1r2 = 0 Solving -25 + -1r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -1r2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1r2 = 0 + 25 -1r2 = 0 + 25 Combine like terms: 0 + 25 = 25 -1r2 = 25 Divide each side by '-1'. r2 = -25 Simplifying r2 = -25 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 '(2 + -1r2)' equal to zero and attempt to solve: Simplifying 2 + -1r2 = 0 Solving 2 + -1r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1r2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1r2 = 0 + -2 -1r2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1r2 = -2 Divide each side by '-1'. r2 = 2 Simplifying r2 = 2 Take the square root of each side: r = {-1.414213562, 1.414213562}Solution
r = {-1.414213562, 1.414213562}
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