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Simplifying 4f2 + 16fg + -9g2 = 0 Reorder the terms: 16fg + 4f2 + -9g2 = 0 Solving 16fg + 4f2 + -9g2 = 0 Solving for variable 'f'. Factor a trinomial. (2f + -1g)(2f + 9g) = 0Subproblem 1
Set the factor '(2f + -1g)' equal to zero and attempt to solve: Simplifying 2f + -1g = 0 Solving 2f + -1g = 0 Move all terms containing f to the left, all other terms to the right. Add 'g' to each side of the equation. 2f + -1g + g = 0 + g Combine like terms: -1g + g = 0 2f + 0 = 0 + g 2f = 0 + g Remove the zero: 2f = g Divide each side by '2'. f = 0.5g Simplifying f = 0.5gSubproblem 2
Set the factor '(2f + 9g)' equal to zero and attempt to solve: Simplifying 2f + 9g = 0 Solving 2f + 9g = 0 Move all terms containing f to the left, all other terms to the right. Add '-9g' to each side of the equation. 2f + 9g + -9g = 0 + -9g Combine like terms: 9g + -9g = 0 2f + 0 = 0 + -9g 2f = 0 + -9g Remove the zero: 2f = -9g Divide each side by '2'. f = -4.5g Simplifying f = -4.5gSolution
f = {0.5g, -4.5g}
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