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Simplifying 2r2 = r + 21 Reorder the terms: 2r2 = 21 + r Solving 2r2 = 21 + r Solving for variable 'r'. Reorder the terms: -21 + -1r + 2r2 = 21 + r + -21 + -1r Reorder the terms: -21 + -1r + 2r2 = 21 + -21 + r + -1r Combine like terms: 21 + -21 = 0 -21 + -1r + 2r2 = 0 + r + -1r -21 + -1r + 2r2 = r + -1r Combine like terms: r + -1r = 0 -21 + -1r + 2r2 = 0 Factor a trinomial. (-3 + -1r)(7 + -2r) = 0Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve: Simplifying -3 + -1r = 0 Solving -3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1r = 0 + 3 -1r = 0 + 3 Combine like terms: 0 + 3 = 3 -1r = 3 Divide each side by '-1'. r = -3 Simplifying r = -3Subproblem 2
Set the factor '(7 + -2r)' equal to zero and attempt to solve: Simplifying 7 + -2r = 0 Solving 7 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2r = 0 + -7 -2r = 0 + -7 Combine like terms: 0 + -7 = -7 -2r = -7 Divide each side by '-2'. r = 3.5 Simplifying r = 3.5Solution
r = {-3, 3.5}
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