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Simplifying 49r2 + 42rs + -112s2 = 0 Reorder the terms: 42rs + 49r2 + -112s2 = 0 Solving 42rs + 49r2 + -112s2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '7'. 7(6rs + 7r2 + -16s2) = 0 Factor a trinomial. 7((7r + -8s)(r + 2s)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(7r + -8s)' equal to zero and attempt to solve: Simplifying 7r + -8s = 0 Solving 7r + -8s = 0 Move all terms containing r to the left, all other terms to the right. Add '8s' to each side of the equation. 7r + -8s + 8s = 0 + 8s Combine like terms: -8s + 8s = 0 7r + 0 = 0 + 8s 7r = 0 + 8s Remove the zero: 7r = 8s Divide each side by '7'. r = 1.142857143s Simplifying r = 1.142857143sSubproblem 2
Set the factor '(r + 2s)' equal to zero and attempt to solve: Simplifying r + 2s = 0 Solving r + 2s = 0 Move all terms containing r to the left, all other terms to the right. Add '-2s' to each side of the equation. r + 2s + -2s = 0 + -2s Combine like terms: 2s + -2s = 0 r + 0 = 0 + -2s r = 0 + -2s Remove the zero: r = -2s Simplifying r = -2sSolution
r = {1.142857143s, -2s}
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