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Simplifying r4 + -12r2 = -35 Reorder the terms: -12r2 + r4 = -35 Solving -12r2 + r4 = -35 Solving for variable 'r'. Reorder the terms: 35 + -12r2 + r4 = -35 + 35 Combine like terms: -35 + 35 = 0 35 + -12r2 + r4 = 0 Factor a trinomial. (5 + -1r2)(7 + -1r2) = 0Subproblem 1
Set the factor '(5 + -1r2)' equal to zero and attempt to solve: Simplifying 5 + -1r2 = 0 Solving 5 + -1r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1r2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1r2 = 0 + -5 -1r2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1r2 = -5 Divide each side by '-1'. r2 = 5 Simplifying r2 = 5 Take the square root of each side: r = {-2.236067978, 2.236067978}Subproblem 2
Set the factor '(7 + -1r2)' equal to zero and attempt to solve: Simplifying 7 + -1r2 = 0 Solving 7 + -1r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1r2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1r2 = 0 + -7 -1r2 = 0 + -7 Combine like terms: 0 + -7 = -7 -1r2 = -7 Divide each side by '-1'. r2 = 7 Simplifying r2 = 7 Take the square root of each side: r = {-2.645751311, 2.645751311}Solution
r = {-2.236067978, 2.236067978, -2.645751311, 2.645751311}
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