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