1. **State the problem:** Rewrite the quadratic function $$f(x) = x^2 + x - 30$$ by completing the square. 2. **Recall the formula:** To complete the square for a quadratic $$ax^2 + bx + c$$ with $$a=1$$, use: $$f(x) = (x + \frac{b}{2})^2 - \left(\frac{b}{2}\right)^2 + c$$ 3. **Identify coefficients:** Here, $$a=1$$, $$b=1$$, and $$c=-30$$. 4. **Calculate $$\frac{b}{2}$$:** $$\frac{1}{2} = 0.5$$ 5. **Square $$\frac{b}{2}$$:** $$\left(0.5\right)^2 = 0.25$$ 6. **Rewrite the function:** $$f(x) = (x + 0.5)^2 - 0.25 - 30$$ 7. **Simplify the constant term:** $$-0.25 - 30 = -30.25$$ 8. **Final completed square form:** $$f(x) = (x + 0.5)^2 - 30.25$$ Thus, the function rewritten by completing the square is: $$f(x) = 1(x + 0.5)^2 - 30.25$$