1. Stating the problem: Solve the equation $$7 f^2 = 84$$ for $f$. 2. Formula and rules: To solve for $f$, isolate $f^2$ by dividing both sides by 7. 3. Intermediate work: $$7 f^2 = 84$$ Divide both sides by 7: $$\cancel{7} f^2 = \frac{84}{\cancel{7}}$$ $$f^2 = 12$$ 4. To find $f$, take the square root of both sides: $$f = \pm \sqrt{12}$$ Simplify the square root: $$f = \pm \sqrt{4 \times 3} = \pm 2\sqrt{3}$$ 5. Final answer: $$f = \pm 2\sqrt{3}$$ This means $f$ can be either positive or negative $2\sqrt{3}$ because squaring either value gives 12.