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Simplifying 0 = 4r2 + -52r + 169 Reorder the terms: 0 = 169 + -52r + 4r2 Solving 0 = 169 + -52r + 4r2 Solving for variable 'r'. Combine like terms: 0 + -169 = -169 -169 + 52r + -4r2 = 169 + -52r + 4r2 + -169 + 52r + -4r2 Reorder the terms: -169 + 52r + -4r2 = 169 + -169 + -52r + 52r + 4r2 + -4r2 Combine like terms: 169 + -169 = 0 -169 + 52r + -4r2 = 0 + -52r + 52r + 4r2 + -4r2 -169 + 52r + -4r2 = -52r + 52r + 4r2 + -4r2 Combine like terms: -52r + 52r = 0 -169 + 52r + -4r2 = 0 + 4r2 + -4r2 -169 + 52r + -4r2 = 4r2 + -4r2 Combine like terms: 4r2 + -4r2 = 0 -169 + 52r + -4r2 = 0 Factor a trinomial. (-13 + 2r)(13 + -2r) = 0Subproblem 1
Set the factor '(-13 + 2r)' equal to zero and attempt to solve: Simplifying -13 + 2r = 0 Solving -13 + 2r = 0 Move all terms containing r to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 2r = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2r = 0 + 13 2r = 0 + 13 Combine like terms: 0 + 13 = 13 2r = 13 Divide each side by '2'. r = 6.5 Simplifying r = 6.5Subproblem 2
Set the factor '(13 + -2r)' equal to zero and attempt to solve: Simplifying 13 + -2r = 0 Solving 13 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2r = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2r = 0 + -13 -2r = 0 + -13 Combine like terms: 0 + -13 = -13 -2r = -13 Divide each side by '-2'. r = 6.5 Simplifying r = 6.5Solution
r = {6.5, 6.5}
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