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Simplifying t2 + 4tf + -21f2 = 0 Reorder the terms: 4ft + -21f2 + t2 = 0 Solving 4ft + -21f2 + t2 = 0 Solving for variable 'f'. Factor a trinomial. (-7f + -1t)(3f + -1t) = 0Subproblem 1
Set the factor '(-7f + -1t)' equal to zero and attempt to solve: Simplifying -7f + -1t = 0 Solving -7f + -1t = 0 Move all terms containing f to the left, all other terms to the right. Add 't' to each side of the equation. -7f + -1t + t = 0 + t Combine like terms: -1t + t = 0 -7f + 0 = 0 + t -7f = 0 + t Remove the zero: -7f = t Divide each side by '-7'. f = -0.1428571429t Simplifying f = -0.1428571429tSubproblem 2
Set the factor '(3f + -1t)' equal to zero and attempt to solve: Simplifying 3f + -1t = 0 Solving 3f + -1t = 0 Move all terms containing f to the left, all other terms to the right. Add 't' to each side of the equation. 3f + -1t + t = 0 + t Combine like terms: -1t + t = 0 3f + 0 = 0 + t 3f = 0 + t Remove the zero: 3f = t Divide each side by '3'. f = 0.3333333333t Simplifying f = 0.3333333333tSolution
f = {-0.1428571429t, 0.3333333333t}
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