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Simplifying 4r2 + 25r + 32 = 7 Reorder the terms: 32 + 25r + 4r2 = 7 Solving 32 + 25r + 4r2 = 7 Solving for variable 'r'. Reorder the terms: 32 + -7 + 25r + 4r2 = 7 + -7 Combine like terms: 32 + -7 = 25 25 + 25r + 4r2 = 7 + -7 Combine like terms: 7 + -7 = 0 25 + 25r + 4r2 = 0 Factor a trinomial. (5 + r)(5 + 4r) = 0Subproblem 1
Set the factor '(5 + r)' equal to zero and attempt to solve: Simplifying 5 + r = 0 Solving 5 + r = 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 + r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + r = 0 + -5 r = 0 + -5 Combine like terms: 0 + -5 = -5 r = -5 Simplifying r = -5Subproblem 2
Set the factor '(5 + 4r)' equal to zero and attempt to solve: Simplifying 5 + 4r = 0 Solving 5 + 4r = 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 + 4r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4r = 0 + -5 4r = 0 + -5 Combine like terms: 0 + -5 = -5 4r = -5 Divide each side by '4'. r = -1.25 Simplifying r = -1.25Solution
r = {-5, -1.25}
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