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Simplifying 21r2 + 35r + 7 = -7r2 Reorder the terms: 7 + 35r + 21r2 = -7r2 Solving 7 + 35r + 21r2 = -7r2 Solving for variable 'r'. Combine like terms: 21r2 + 7r2 = 28r2 7 + 35r + 28r2 = -7r2 + 7r2 Combine like terms: -7r2 + 7r2 = 0 7 + 35r + 28r2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(1 + 5r + 4r2) = 0 Factor a trinomial. 7((1 + r)(1 + 4r)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + r)' equal to zero and attempt to solve: Simplifying 1 + r = 0 Solving 1 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + r = 0 + -1 r = 0 + -1 Combine like terms: 0 + -1 = -1 r = -1 Simplifying r = -1Subproblem 2
Set the factor '(1 + 4r)' equal to zero and attempt to solve: Simplifying 1 + 4r = 0 Solving 1 + 4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4r = 0 + -1 4r = 0 + -1 Combine like terms: 0 + -1 = -1 4r = -1 Divide each side by '4'. r = -0.25 Simplifying r = -0.25Solution
r = {-1, -0.25}
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