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Simplifying r2 + 19rs + 90s2 = (r + 10)(r + 9s2) Reorder the terms: 19rs + r2 + 90s2 = (r + 10)(r + 9s2) Reorder the terms: 19rs + r2 + 90s2 = (10 + r)(r + 9s2) Multiply (10 + r) * (r + 9s2) 19rs + r2 + 90s2 = (10(r + 9s2) + r(r + 9s2)) 19rs + r2 + 90s2 = ((r * 10 + 9s2 * 10) + r(r + 9s2)) 19rs + r2 + 90s2 = ((10r + 90s2) + r(r + 9s2)) 19rs + r2 + 90s2 = (10r + 90s2 + (r * r + 9s2 * r)) Reorder the terms: 19rs + r2 + 90s2 = (10r + 90s2 + (9rs2 + r2)) 19rs + r2 + 90s2 = (10r + 90s2 + (9rs2 + r2)) Reorder the terms: 19rs + r2 + 90s2 = (10r + 9rs2 + r2 + 90s2) 19rs + r2 + 90s2 = (10r + 9rs2 + r2 + 90s2) Add '-1r2' to each side of the equation. 19rs + r2 + -1r2 + 90s2 = 10r + 9rs2 + r2 + -1r2 + 90s2 Combine like terms: r2 + -1r2 = 0 19rs + 0 + 90s2 = 10r + 9rs2 + r2 + -1r2 + 90s2 19rs + 90s2 = 10r + 9rs2 + r2 + -1r2 + 90s2 Combine like terms: r2 + -1r2 = 0 19rs + 90s2 = 10r + 9rs2 + 0 + 90s2 19rs + 90s2 = 10r + 9rs2 + 90s2 Add '-90s2' to each side of the equation. 19rs + 90s2 + -90s2 = 10r + 9rs2 + 90s2 + -90s2 Combine like terms: 90s2 + -90s2 = 0 19rs + 0 = 10r + 9rs2 + 90s2 + -90s2 19rs = 10r + 9rs2 + 90s2 + -90s2 Combine like terms: 90s2 + -90s2 = 0 19rs = 10r + 9rs2 + 0 19rs = 10r + 9rs2 Solving 19rs = 10r + 9rs2 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10r' to each side of the equation. -10r + 19rs = 10r + -10r + 9rs2 Combine like terms: 10r + -10r = 0 -10r + 19rs = 0 + 9rs2 -10r + 19rs = 9rs2 Add '-9rs2' to each side of the equation. -10r + 19rs + -9rs2 = 9rs2 + -9rs2 Combine like terms: 9rs2 + -9rs2 = 0 -10r + 19rs + -9rs2 = 0 Factor out the Greatest Common Factor (GCF), 'r'. r(-10 + 19s + -9s2) = 0 Factor a trinomial. r((-10 + 9s)(1 + -1s)) = 0Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
Set the factor '(-10 + 9s)' equal to zero and attempt to solve: Simplifying -10 + 9s = 0 Solving -10 + 9s = 0 Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + 9s = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 9s = 0 + 10 9s = 0 + 10 Combine like terms: 0 + 10 = 10 9s = 10 Add '-9s' to each side of the equation. 9s + -9s = 10 + -9s Combine like terms: 9s + -9s = 0 0 = 10 + -9s Simplifying 0 = 10 + -9s The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + -1s)' equal to zero and attempt to solve: Simplifying 1 + -1s = 0 Solving 1 + -1s = 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 + -1s = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1s = 0 + -1 -1s = 0 + -1 Combine like terms: 0 + -1 = -1 -1s = -1 Add 's' to each side of the equation. -1s + s = -1 + s Combine like terms: -1s + s = 0 0 = -1 + s Simplifying 0 = -1 + s The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
r = {0}
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