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Simplifying (r + -2)(r + 7) + (r + -2)(r + 2) = 0 Reorder the terms: (-2 + r)(r + 7) + (r + -2)(r + 2) = 0 Reorder the terms: (-2 + r)(7 + r) + (r + -2)(r + 2) = 0 Multiply (-2 + r) * (7 + r) (-2(7 + r) + r(7 + r)) + (r + -2)(r + 2) = 0 ((7 * -2 + r * -2) + r(7 + r)) + (r + -2)(r + 2) = 0 ((-14 + -2r) + r(7 + r)) + (r + -2)(r + 2) = 0 (-14 + -2r + (7 * r + r * r)) + (r + -2)(r + 2) = 0 (-14 + -2r + (7r + r2)) + (r + -2)(r + 2) = 0 Combine like terms: -2r + 7r = 5r (-14 + 5r + r2) + (r + -2)(r + 2) = 0 Reorder the terms: -14 + 5r + r2 + (-2 + r)(r + 2) = 0 Reorder the terms: -14 + 5r + r2 + (-2 + r)(2 + r) = 0 Multiply (-2 + r) * (2 + r) -14 + 5r + r2 + (-2(2 + r) + r(2 + r)) = 0 -14 + 5r + r2 + ((2 * -2 + r * -2) + r(2 + r)) = 0 -14 + 5r + r2 + ((-4 + -2r) + r(2 + r)) = 0 -14 + 5r + r2 + (-4 + -2r + (2 * r + r * r)) = 0 -14 + 5r + r2 + (-4 + -2r + (2r + r2)) = 0 Combine like terms: -2r + 2r = 0 -14 + 5r + r2 + (-4 + 0 + r2) = 0 -14 + 5r + r2 + (-4 + r2) = 0 Reorder the terms: -14 + -4 + 5r + r2 + r2 = 0 Combine like terms: -14 + -4 = -18 -18 + 5r + r2 + r2 = 0 Combine like terms: r2 + r2 = 2r2 -18 + 5r + 2r2 = 0 Solving -18 + 5r + 2r2 = 0 Solving for variable 'r'. Factor a trinomial. (-9 + -2r)(2 + -1r) = 0Subproblem 1
Set the factor '(-9 + -2r)' equal to zero and attempt to solve: Simplifying -9 + -2r = 0 Solving -9 + -2r = 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 + -2r = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2r = 0 + 9 -2r = 0 + 9 Combine like terms: 0 + 9 = 9 -2r = 9 Divide each side by '-2'. r = -4.5 Simplifying r = -4.5Subproblem 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 = {-4.5, 2}
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