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Simplifying 7r2 + 14r + -50 = 6 Reorder the terms: -50 + 14r + 7r2 = 6 Solving -50 + 14r + 7r2 = 6 Solving for variable 'r'. Reorder the terms: -50 + -6 + 14r + 7r2 = 6 + -6 Combine like terms: -50 + -6 = -56 -56 + 14r + 7r2 = 6 + -6 Combine like terms: 6 + -6 = 0 -56 + 14r + 7r2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-8 + 2r + r2) = 0 Factor a trinomial. 7((-4 + -1r)(2 + -1r)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve: Simplifying -4 + -1r = 0 Solving -4 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1r = 0 + 4 -1r = 0 + 4 Combine like terms: 0 + 4 = 4 -1r = 4 Divide each side by '-1'. r = -4 Simplifying r = -4Subproblem 2
Set the factor '(2 + -1r)' equal to zero and attempt to solve: Simplifying 2 + -1r = 0 Solving 2 + -1r = 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 + -1r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1r = 0 + -2 -1r = 0 + -2 Combine like terms: 0 + -2 = -2 -1r = -2 Divide each side by '-1'. r = 2 Simplifying r = 2Solution
r = {-4, 2}
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