Question: You are trying to solve the quadratic equation $x^2 - 10x = 30$. After completing the square, which of the following is the resulting equation? $x^2 - 10x - 100 = -70$, $x^2 - 10x + 100 = 130$, $x^2 - 10x - 25 = 5$, $x^2 - 10x + 25 = 55$
1. **State the problem:** We want to solve the quadratic equation $$x^2 - 10x = 30$$ by completing the square.
2. **Recall the formula for completing the square:** For an equation of the form $$x^2 + bx = c$$, we add $$\left(\frac{b}{2}\right)^2$$ to both sides to form a perfect square trinomial on the left.
3. **Identify $b$:** Here, $b = -10$.
4. **Calculate $\left(\frac{b}{2}\right)^2$:**
$$\left(\frac{-10}{2}\right)^2 = (-5)^2 = 25$$
5. **Add 25 to both sides:**
$$x^2 - 10x + 25 = 30 + 25$$
6. **Simplify the right side:**
$$x^2 - 10x + 25 = 55$$
7. **Result:** The equation after completing the square is $$x^2 - 10x + 25 = 55$$.
8. **Check the options:** The correct choice is the last one: $$x^2 - 10x + 25 = 55$$.