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Simplifying -4r2 + -10r + 52 = 2 Reorder the terms: 52 + -10r + -4r2 = 2 Solving 52 + -10r + -4r2 = 2 Solving for variable 'r'. Reorder the terms: 52 + -2 + -10r + -4r2 = 2 + -2 Combine like terms: 52 + -2 = 50 50 + -10r + -4r2 = 2 + -2 Combine like terms: 2 + -2 = 0 50 + -10r + -4r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -5r + -2r2) = 0 Factor a trinomial. 2((5 + -2r)(5 + r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -2r)' equal to zero and attempt to solve: Simplifying 5 + -2r = 0 Solving 5 + -2r = 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 + -2r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2r = 0 + -5 -2r = 0 + -5 Combine like terms: 0 + -5 = -5 -2r = -5 Divide each side by '-2'. r = 2.5 Simplifying r = 2.5Subproblem 2
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 = -5Solution
r = {2.5, -5}
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