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Simplifying r2 + -9r + -45 = 7 Reorder the terms: -45 + -9r + r2 = 7 Solving -45 + -9r + r2 = 7 Solving for variable 'r'. Reorder the terms: -45 + -7 + -9r + r2 = 7 + -7 Combine like terms: -45 + -7 = -52 -52 + -9r + r2 = 7 + -7 Combine like terms: 7 + -7 = 0 -52 + -9r + r2 = 0 Factor a trinomial. (-4 + -1r)(13 + -1r) = 0Subproblem 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 '(13 + -1r)' equal to zero and attempt to solve: Simplifying 13 + -1r = 0 Solving 13 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1r = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1r = 0 + -13 -1r = 0 + -13 Combine like terms: 0 + -13 = -13 -1r = -13 Divide each side by '-1'. r = 13 Simplifying r = 13Solution
r = {-4, 13}
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