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Simplifying 14r4 + -33r2 + 18 = 0 Reorder the terms: 18 + -33r2 + 14r4 = 0 Solving 18 + -33r2 + 14r4 = 0 Solving for variable 'r'. Factor a trinomial. (6 + -7r2)(3 + -2r2) = 0Subproblem 1
Set the factor '(6 + -7r2)' equal to zero and attempt to solve: Simplifying 6 + -7r2 = 0 Solving 6 + -7r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7r2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7r2 = 0 + -6 -7r2 = 0 + -6 Combine like terms: 0 + -6 = -6 -7r2 = -6 Divide each side by '-7'. r2 = 0.8571428571 Simplifying r2 = 0.8571428571 Take the square root of each side: r = {-0.9258201, 0.9258201}Subproblem 2
Set the factor '(3 + -2r2)' equal to zero and attempt to solve: Simplifying 3 + -2r2 = 0 Solving 3 + -2r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2r2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2r2 = 0 + -3 -2r2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2r2 = -3 Divide each side by '-2'. r2 = 1.5 Simplifying r2 = 1.5 Take the square root of each side: r = {-1.224744871, 1.224744871}Solution
r = {-0.9258201, 0.9258201, -1.224744871, 1.224744871}
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