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Simplifying 28r2 + 88r + 64 = 0 Reorder the terms: 64 + 88r + 28r2 = 0 Solving 64 + 88r + 28r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(16 + 22r + 7r2) = 0 Factor a trinomial. 4((2 + r)(8 + 7r)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + r)' equal to zero and attempt to solve: Simplifying 2 + r = 0 Solving 2 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + r = 0 + -2 r = 0 + -2 Combine like terms: 0 + -2 = -2 r = -2 Simplifying r = -2Subproblem 2
Set the factor '(8 + 7r)' equal to zero and attempt to solve: Simplifying 8 + 7r = 0 Solving 8 + 7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 7r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7r = 0 + -8 7r = 0 + -8 Combine like terms: 0 + -8 = -8 7r = -8 Divide each side by '7'. r = -1.142857143 Simplifying r = -1.142857143Solution
r = {-2, -1.142857143}
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