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Simplifying 12s2 + -29sb + 14b2 = 0 Reorder the terms: -29bs + 14b2 + 12s2 = 0 Solving -29bs + 14b2 + 12s2 = 0 Solving for variable 'b'. Factor a trinomial. (2b + -3s)(7b + -4s) = 0Subproblem 1
Set the factor '(2b + -3s)' equal to zero and attempt to solve: Simplifying 2b + -3s = 0 Solving 2b + -3s = 0 Move all terms containing b to the left, all other terms to the right. Add '3s' to each side of the equation. 2b + -3s + 3s = 0 + 3s Combine like terms: -3s + 3s = 0 2b + 0 = 0 + 3s 2b = 0 + 3s Remove the zero: 2b = 3s Divide each side by '2'. b = 1.5s Simplifying b = 1.5sSubproblem 2
Set the factor '(7b + -4s)' equal to zero and attempt to solve: Simplifying 7b + -4s = 0 Solving 7b + -4s = 0 Move all terms containing b to the left, all other terms to the right. Add '4s' to each side of the equation. 7b + -4s + 4s = 0 + 4s Combine like terms: -4s + 4s = 0 7b + 0 = 0 + 4s 7b = 0 + 4s Remove the zero: 7b = 4s Divide each side by '7'. b = 0.5714285714s Simplifying b = 0.5714285714sSolution
b = {1.5s, 0.5714285714s}
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