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Simplifying 7r2 = -42r + 112 Reorder the terms: 7r2 = 112 + -42r Solving 7r2 = 112 + -42r Solving for variable 'r'. Reorder the terms: -112 + 42r + 7r2 = 112 + -42r + -112 + 42r Reorder the terms: -112 + 42r + 7r2 = 112 + -112 + -42r + 42r Combine like terms: 112 + -112 = 0 -112 + 42r + 7r2 = 0 + -42r + 42r -112 + 42r + 7r2 = -42r + 42r Combine like terms: -42r + 42r = 0 -112 + 42r + 7r2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-16 + 6r + r2) = 0 Factor a trinomial. 7((-8 + -1r)(2 + -1r)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-8 + -1r)' equal to zero and attempt to solve: Simplifying -8 + -1r = 0 Solving -8 + -1r = 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 + -1r = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1r = 0 + 8 -1r = 0 + 8 Combine like terms: 0 + 8 = 8 -1r = 8 Divide each side by '-1'. r = -8 Simplifying r = -8Subproblem 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 = {-8, 2}
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