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Simplifying 8r2 = -16r + 90 Reorder the terms: 8r2 = 90 + -16r Solving 8r2 = 90 + -16r Solving for variable 'r'. Reorder the terms: -90 + 16r + 8r2 = 90 + -16r + -90 + 16r Reorder the terms: -90 + 16r + 8r2 = 90 + -90 + -16r + 16r Combine like terms: 90 + -90 = 0 -90 + 16r + 8r2 = 0 + -16r + 16r -90 + 16r + 8r2 = -16r + 16r Combine like terms: -16r + 16r = 0 -90 + 16r + 8r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + 8r + 4r2) = 0 Factor a trinomial. 2((-9 + -2r)(5 + -2r)) = 0 Ignore the factor 2.Subproblem 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 '(5 + -2r)' equal to zero and attempt to solve: Simplifying 5 + -2r = 0 Solving 5 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2r = 0 + -5 -2r = 0 + -5 Combine like terms: 0 + -5 = -5 -2r = -5 Divide each side by '-2'. r = 2.5 Simplifying r = 2.5Solution
r = {-4.5, 2.5}
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