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Simplifying r(14r + 5) = 9 Reorder the terms: r(5 + 14r) = 9 (5 * r + 14r * r) = 9 (5r + 14r2) = 9 Solving 5r + 14r2 = 9 Solving for variable 'r'. Reorder the terms: -9 + 5r + 14r2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 5r + 14r2 = 0 Factor a trinomial. (-1 + -1r)(9 + -14r) = 0Subproblem 1
Set the factor '(-1 + -1r)' equal to zero and attempt to solve: Simplifying -1 + -1r = 0 Solving -1 + -1r = 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 + -1r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1r = 0 + 1 -1r = 0 + 1 Combine like terms: 0 + 1 = 1 -1r = 1 Divide each side by '-1'. r = -1 Simplifying r = -1Subproblem 2
Set the factor '(9 + -14r)' equal to zero and attempt to solve: Simplifying 9 + -14r = 0 Solving 9 + -14r = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -14r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -14r = 0 + -9 -14r = 0 + -9 Combine like terms: 0 + -9 = -9 -14r = -9 Divide each side by '-14'. r = 0.6428571429 Simplifying r = 0.6428571429Solution
r = {-1, 0.6428571429}
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