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Simplifying 4r2 = 102 + -7r Solving 4r2 = 102 + -7r Solving for variable 'r'. Reorder the terms: -102 + 7r + 4r2 = 102 + -7r + -102 + 7r Reorder the terms: -102 + 7r + 4r2 = 102 + -102 + -7r + 7r Combine like terms: 102 + -102 = 0 -102 + 7r + 4r2 = 0 + -7r + 7r -102 + 7r + 4r2 = -7r + 7r Combine like terms: -7r + 7r = 0 -102 + 7r + 4r2 = 0 Factor a trinomial. (-6 + -1r)(17 + -4r) = 0Subproblem 1
Set the factor '(-6 + -1r)' equal to zero and attempt to solve: Simplifying -6 + -1r = 0 Solving -6 + -1r = 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 + -1r = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1r = 0 + 6 -1r = 0 + 6 Combine like terms: 0 + 6 = 6 -1r = 6 Divide each side by '-1'. r = -6 Simplifying r = -6Subproblem 2
Set the factor '(17 + -4r)' equal to zero and attempt to solve: Simplifying 17 + -4r = 0 Solving 17 + -4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -4r = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -4r = 0 + -17 -4r = 0 + -17 Combine like terms: 0 + -17 = -17 -4r = -17 Divide each side by '-4'. r = 4.25 Simplifying r = 4.25Solution
r = {-6, 4.25}
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